Used to be, back in the early '30s, anti-tank rounds were commonly small (the .50-cal Browning MG was the standard American anti-tank weapon at the time). In that case...yes, things that got through the armor would bounce around a bit and maybe hit someone.
Modern tanks and anti-tank weapons...well, ever see footage of the Iraqi T-72s being hit by American weapons, even "small" ones like the 30mm gun on the A-10? They pretty much explode. Modern anti-tank weapons put so much energy on target...like BiB said, doesn't really matter. If it can get through tank armor, a flak vest isn't going to help.