WARNING: If "trying this at home" be aware that there is a small potential for significant hazard occurring - see below.
What you propose is a viable and useful and potentially dangerous method.
I consider it is extremely unlikely that you will harm yourself doing this but need to note that the possibility exists.
I would not do this with other than single Alkaline or NiMh cells. I would be extremely careful with cells above AA in size. I would not consider trying this with LiIon or LiPo of LiFePO4 cells - which all have higher terminal voltages, high potential discharge rates, and a known tendency (except for LiFePO4) to "vent with flames".
I have used the method for testing partially used Alkaline batteries for many years with good success. I have never had any problems with it BUT this does not mean that everyone else will be so lucky. Comments at end re what might go wrong.
To determine the "degree of goodness" of an Alkaline AA 1.5V battery I do two things.
Measure cell open circuit potential. This is a very safe and non damaging method. An unused Alkaline battery that has not used up much of its shelf life will have more than 1.6V potential - typically 1.65V. This is higher than the cheaper Carbon-Zinc / Le Clanche / Heavy duty cells and is a reliable way of determining both that a cell really IS an Alkaline one and that it is essentially new. A cell that gives more than 1.6V does not need to be "tested" by current discharge as described below (but can be if desired).
Measure cell short circuit current for about one second using the 10 amp range on a multimeter. The meter's internal resistance, lead resistances, plug in connection resistances and contact resistance with the battery all are potentially significant resistances in this test so the results will vary somewhat between meters and depending on how well the probes make contact and how well the lead-plugs make contact in the meter sockets. Despite these potential differences (pun noted) the test is useful and reasonably repeatable.
Information only: My most usual reason for doing this test is to determine which cells in a batch of cells are unused, and which of the used ones are suitable for use in a high output camera flash. The flashes concerned present a heavy load. Capacity is probably around 100 flashes - depending on energy taken which varies with photo environment - a flash into a dark large room takes a full charge whereas when photographing a light coloured subject at close range only a small fraction of the stored energy is used. When used repeatedly to exhaustion the batteries are too hot to handle when removed from the flash - probably 70 degrees C ! The average power supplied by the batteries at full load is probably 50 to 100 Watts. The batteries need to be in good condition to supply this.
The short-circuit test typically returns a result of 5 to 10 amps for good quality new cells, with the current falling slightly during the approximately one second test period.
The results for used cells varies considerably. Anything in the 3 to 5 amp range means that the cell is liable to be useful for flash use. A result of a few amps means the battery is still useful for low drain equipment such as a clock or electronic scales. Less than that the cell is probably best discarded.
While the above test is used for AA Alkaline cells it is also usable for NimH AA cells - with more risk. A NimH cell MAY be capable of higher discharge rates when fully charged, although the resistances present in this test will usually limit current to about the same values. I just tried this with a fully charged 2000 mAh Eneloop AA cell (Panasonic Chinese made version). This peaked at about 7 amps. The Eneloop cells are of lower capacity than the market leading quality AA NimH cells, but have a much longer shelf life and higher terminal voltage at given discharge level. I'd expect them to give similar results to higher capacity "normal" AA NimH cells.
On a few occasions I have been silly enough to carry cells in my trouser pocket a number of charged AA cells and on 3 such occasions was also unlucky enough to have them form a stable circuit with various coins, keys etc in my pocket. Pocket temperatures rose to well above pain level nearly instantly and burns were a definite possibility. Pocket contents had to be shed with indecent hast on each occasion. While no cell ever gave any indication of mechanical damage, if one had 'exploded' in some fashion under such abuse I'd have been the sorrier but not surprised.
A meter set to 10A is unlikely to be damaged by shorting a single AA NimH cell for short periods. More than one cell in series or larger than AA may cause dismemberment of cell or conflagration or dismemberment of meter internals. Some meters are fused on their 10A range but many are not (and most cheap ones that I have seen are not). Extended 10A range over-current use may destroy the 10A shunt and possibly the meter itself a few milliseconds later.
Hard shorts on batteries MAY cause disproportionate decreases in capacity compared to actual energy taken and MAY cause long term permanent degradation in secondary cells. I have not noticed that this is the case but YMMV.
After shorting the Eneloop cell mentioned above for a total of about 5 seconds at 7A it took about 40 mAh of charge to restore it to full capacity. Energy out ~= 1V say x 7A x5 seconds = 35 Joules. Restoration energy ~~= 1.4V x 40 mAh ~= 200 Joules. This test sample (1 item) is too small and uncontrolled to allow any good conclusion, but is interesting.
Worst case it seems likely that under full short circuit a cell may dissipate around 10 Watts internally, and usually less than that. My informal inadvertent pocket testing of NimH cells under high discharge for probably 10-20s indicates that they will tolerate this without self-dismantlement (at least for the small sample I have experienced), and my use if a flash on many occasions of AA Alkaline cells so that they become too hot to handle suggests that that too tolerate heavy discharge and high temperatures "well enough".
So, I would not expect that short circuit testing any AA Alkaline or NimH cell as described above would be physically dangerous. But if it ever did turn out to be, I would not be totally surprised.