Blower Motor Heat and Cool Control Board
It'd be fine, simply because I can't think of a 120 volt AC relay that would be damaged by getting back fed power. Mechanical and solid state can both handle it as far as I know. That's not a 100% you're good though, maybe 90+% confidence? 

Worst case it passes current backwards through to hot and won't be able to shut itself off, but you'll catch that during testing. Nothing should blow up.