Does the body diode in MOSFET conduct current in backward direction when the MOSFET is switched OFF? If yes, can we build rectifier-bridge using 4 non-driven MOSFETs?
...at least according to the US patent US5302858, containing the following illustration:
This is used in at least one uninterruptible power supply, for providing a rectified charging voltage to the battery using the same transistors as are used when generating an AC output from the battery.
This information comes from a "teardown video" by Dave Jones at EEVblog, which contains more details about the operation of one particular UPS.
If you can do the same thing using other transistors is a different question. It is unknown if the designers of the UPS in question characterized a specific MOSFET model on their own, or perhaps they got this information by the manufacturer of the MOSFETs.
If you try hard enough, you might be able to squeeze blood out of a turnip.
Seriously, most mosfets made today have high-current snubber diodes built in which intentionally allow reverse currents to bypass the mosfet so it is not damaged. Mosfets for synchronous rectification do not have this snubber diode (though they still have 'parasitic' diodes as a natural part of their construction), but are used for supplies less <= 6 volts, where the .5 volt drop of a schottky diode is a bit too much.
Unless the desired voltage is 6 volts or less, use the 1N4007 series for 1 amp max current, or 1N5408 for 3 amps or 6A10 for 6 amps. These are good up to 1KV at 4KHZ sine wave.
For switch mode supplies use schottky diodes for voltages <= 24vdc. A 1N5822-T is rated for 40 volts at 3 amps and is good for some LED driver circuits and many if not most general purpose power supplies.
The BAT46 is rated for 100v 150mA and is normally used for isolated current detection or a flyback boost supply, or a bias/supply for low-current devices, including some LED strings.
The FEP16DT-E3 is rated 200v at 2 x 8 amps in a 3 pin TO-220 package. Can be used in parallel for a 16 amp rating or as a summing diode.
The FRUS20TM4S is a fast medium voltage (<1KV) rectifier for off-line SMPS and is rated 430v at 20 amps. Comes in a TO-220 package and is a bit expensive.
For high-speed low-current the cheap but super-fast 1N4148 is a good choice (100v at 200mA, 4nS, max clock speed is ~50MHZ).
The bottom line is that there is a diode/rectifier for every possible need.
Use mosfets as a mosfet. Your not saving any money or space by using just the internal diode, and it will not impress anyone if you did.