Yes, this is an excellent application for radiant heat as radiated heat bounces off the glass without warming it and the heat is kept inside. A cathedral ceiling increases heat loss due to the extra area, but if it is highly insulated it wouldn't be a major loss. The extra height makes no difference to the radiant floor, it just increases the heat loss of the room, so the floor alone might not be able to provide ALL the heat. You might want to add baseboard along the outer edge if you want to maintain 70F on the porch that would be an independent additional heat if necessary.
I had customers that lived in a boat in Maryland and got used to living in a condo in New Jersey setting the thermostat to the 55F that they were used to.