Sure, it can be done. How involved are you willing to get doing it? It involves changing wires at the BIU and defogger switch and I think changing the switch itself to a mechanical latching one (not sure on this.)
Ah yes. Timer - I did forget about this, but i have turned mine on again right after it shuts off, with no ill affect. I think it depends on temp and water/ice conditions. But you are correct XJ, that not having it on the timer would introduce a new potential failure mode where the car is no longer timing it.
When you're expecting snow/ice (a situation you'd need the rear defroster), crank your heat up to the max before shutting your vehicle off before exiting. Then remote start, as normal...
When you finally go out to your vehicle, before doing anything else, clear the driver door, then manually enable the rear defroster and let it run while you brush off the rest of your car (don't be "that guy" who drives with a pile of snow on the roof that can fly off and destroy a vehicle behind you), leaving the rear windshield for last. By the time you're at the rear windshield, between the interior heater and the rear defroster, you should be able to clear that windshield no problem.
I don't have a remote start on either of my vehicles, and have never had trouble clearing my rear windshield with this method (without the remote start assist in heating the vehicle); it's the front/sides that always give me trouble, since it isn't wired into the glass.
Forgot --- a "time delay relay" installed will replicate the timer in the BIU and if the delay time is set correctly on the relay, will eliminate the potential harm from leaving the switch on. Such relays are available for $10 - $50 ish.