Crouching does not affect either accuracy or recoil.
Tested with a pristine AR16 (without accuracy upgrade) at a range of 20 seconds walking pace. Target was a floating tire in the marina in the south region.
Fired two complete magazines at one-shot intervals, alternating between standing and crouching. Standing position scored hits on 5 rounds out of 15 both times, crouching scored hits 5 and 6 times out of 15 respectively. Difference not statistically significant.
Shotguns tested by firing at a rock in the middle of the marina and counting the number of water splashes around the rock (indicating misses). Total of 24 rounds fired from each position. Standing missed 56 times, crouching missed 55. Difference not statistically significant.
Switched to Uzi (without accuracy upgrade). Aimed at bottom of nearby crate, fired sustained burst. Muzzle climbed to top of crate by the time magazine was exhausted. Crouched, repeated. Muzzle also climbed to top of crate by magazine exhaustion. No measurable difference.
Pistols and sniper rifles not tested since I couldn't find something that would react when shot from a draw distance great enough to provide meaningful data.