I have a full size propane grill in there,
Do you think it will heat
the space from 0 degrees F up to 40 degrees F?

Very dubious. CO2 does not support life.

1) Is there any reason why I shouldn't do this?

It's not very effective, and not especially safe. Wear insulated grubbies when
you work out there. Start by drywalling and insulating the first floor and get
a Modine or similar hanging heater set up for propane or NG, your choice. HTH

Joe