no, only a tiny number of the 172 give a shit about Blair, and if anyone thinks even they would throw themselves under a bus for a PM who left office nearly a decade ago they need to give themselves a bit of a shake.
Chilcot will be a bit embarrassing for some Labour MP's (Hilary Benn was at DFID in 2003), but none of them were in senior positions or got to make big decisions about whether Iraq happened or not - the 'its Chilcot, stupid' stuff is just conspiraloon rubbish pulled out of someones arse to divert attention from the fact that Corbyn is, in fact, crap at his job and that this is as much a reason there are 172 no confidence votes as the fact that they hate his politics. noting, of course, that some of the 172 don't hate his politics, they quite like them - they just think he's crap at his job.
Corbyn - or Watson, or Cooper, or Eagle - could call for the prosecution of Blair for War Crimes, but its not their call, and if Chilcot doesn't find evidence of things that Blair etc.. can actually be prosecuted for (and lying isn't a crime...) then they're just going to look silly.