No reason not to. Go for it and have fun.

nothing wrong with that. Remember though that your pedaling technique improves not necessarily from "just riding" a fixie... it improves from having high forces throughout the pedal stroke [which is why (elite) mtb'ers have really good strokes].

Good point, John. As the story goes (I say it this way because I have never actually experienced a smooth stroke), mtb'ers develop their smooth stroke because they will loose traction when climbing on loose soil if they are stomping or mashing on the pedals. You can simulate these conditions a bit on the trainer by making sure that you haven't tightened the trainer down too tight on your rear wheel. You'll have to play with it a bit to get it right but the goal is to get it tight enough to get traction but loose enough that if you mash or stomp your wheel will slip.

Rusty

Not sure you are going to get that sensation without a flywheel, like on a spinning bike, which has a fixed gear.