Why install a hidden GFCI outlet controlling sink outlets, ceiling lights, vent fan, and floor heater?
It's okay to share other fixtures on the bathroom outlet circuit like the vent fan and lights if the bathroom circuit does not feed outlets in another bathroom.  In your post you mentioned a floor heater which might be temporary and portable, but if it's built-in to the base then that might be a violation of 210.32.(A)(2) which permits 50% of 20 amps or 10 amps or less. If it's portable then the code allows 80% of 20 amps or 16 amps or less.

Other than that a GFCI outlet should always be accessible.  A linen closet isn't an obvious location for starters, and may eventually get hidden behind stuff.