The answer is a resounding yes or maybe.
Yes salvage what you are likely to use in some way for play, study or repairs and maybe don't keep stuff that you will never use.
I find that keeping a couple of old and a couple of contemporary PCBs of the sort that I am likely to work on or experiment with saves a LOT of time compared to ordering or shopping for the odd part that I want to try out. I have very rarely made use of salvaged parts for any kind of production run of more than 2 as it it plain too slow collecting multiples of anything on scrap boards or in the junk boxes.
SMD salvage is difficult to justify and though through hole is becoming scarcer it still has a place in robust electronics.
Also remember to sort the pulls so you can find them speedily when you are in need. Exotic parts are much more useful to pull as generics are easier to buy in assortment kits. Having 1200 resistors (US$10) on tap is much more fun that hunting for a desired value and not finding it.
However of much more value than the components when starting out with repair , design or hobby is the amount of learning you can gain from figuring out what the boards generally (and later more specifically) did and why designers did what they did which will teach you good skills. You will learn to tell which boards were well designed with a glance and pay attention to new tricks they have used and which boards are commodity junk that is a second (or more) generation copy and contains defects or errors that have been copied over badly without understanding what they are doing. Generally industry gets better electronics because they pay more because their equipment makes money, consumers shop by price so they get junk.
It is always fun to see huge mains isolation areas on part of a PCB and then have the mains switch traces routed around to the other side of the PCB alongside all the low voltage circuits with 1mm track spacing.