Dennis wrote:
Unlikely. You would actually have to chance the laws of thermodynamics to
make a difference. One area you might not be considering is that it's not
only against code, it's also more expensive to heat the home. Bath (and
kitchen) fans carry a tremendous amount of moisture. Dump this into the
attic in cool/cold weather will cause this moisture to settle into the
insulation; degrading the performance and moving the dew point closer to the
heated side. It's not out-of-the question to consider a R-value loss of 50%
or more (one test showed much more) on cold days.

This may be a little OT, but if a person was dead set for some reason
on venting to the attic OR they came across such a set-up, you can
simply change your habits to minimize risk of attic condensation.

You entirely missed what I wrote. The whole idea is NOT to dump
moisture into the attic by NOT running the fan during cool outside
conditions.