Yes to the first part of you question. Without specific info, I would say no to the second part.
See 2008 NEC 210.11[C] exception, which refers to 210.23[A] exception, and 210.23[A]. Even if you could, you would be limited to 50% of the branch circuit rating. According to 424.3 though, fixed electric space heating would be a continuous load.
I think most manufactures even recommend an individual branch circuit for the infrared or combo heat/light/vent units as well.
I don’t think it would leave much capacity for those Mega hair dryers and curling irons that all the ladies seem to use these days.