Their aura forces rerolls on all checks. The flat roll to recover counts as a check as far as I'm aware. So yes.
But keep in mind, it's a 20ft range so your friends could try to move you to safety. It's also a misfortune effect, and if you can get a fortune effect placed on you instead, it will cancel out. However, it'd need to be a fortune effect with a duration, as I think otherwise it would only cancel the pugwampi's aura for one check, which would create really difficult timing to get that on you after you go down and before you make the check.