Yes, and they've been used for training for a long time. Lot's of guys train on fixed gear. Locally a couple of them will use flip/flop bikes, go like crazy fixed for 20 miles, then flip 'em and ride back for recovery. Pretty much shreds the legs for a day or so.

"Train heavy, race light" has been around for a long time; but it's given way in many cases to simply adding resistance. Lot's of good criterium riders train on 700x28's running lower pressure, or even a heavy wheelset, as they've found the frame not to me much of a factor. I know a guy who trains on a Cannondale touring bike with front and rear baskets, like a newspaper bike on a diet....He regularly trains at 21-22mph, and often borrows bikes to race. In team triathlons, he's the one you want...

I use a Raleigh Rapide set up as a single-speed with the FD/RD removed, small chainring gone, and bullhorn bars. The hardest thing is to resist the urge to shift.