Can you brew black tea in a macchinetta?
I highly doubt that this practice would damage your macchinetta.  It's a relatively simple device, and with simplicity comes durability.   If finely-ground coffee won't plug the baskets and filters inside, then it's doubtful that much larger tea leaves will.  As with normal (i.e. coffee) use, just ensure that the pressure release valves are unobstructed (you don't want to fill the bottom portion with water past the valve, for example).  You probably want to avoid over-filling the middle basket that normally contains the coffee grounds, too; tea leaves will absorb more moisture and expand more than coffee grounds.  That's the one scenario where I could see the pot becoming plugged, although in that case the lower pressure valve should release the steam before the pot gets damaged.

The temperature of the water inside is probably just about right for black teas, but way too hot for green and other delicate teas.  These can burn at such temperatures and should be avoided, since you can't control the temperature of the steaming water passing through the pot - it will always by definition be boiling.  

Whether you'll get a good extraction compared to steeping is questionable, and it's possible that the pressure which builds up inside the pot will change how flavors get extracted.  A macchinetta does tend to extract more flavor and caffeine from coffee grounds than non-pressurized methods like drip brewing, so a similar effect with tea leaves wouldn't be shocking.  It's worth a try; after all, if someone hadn't tried brewing coffee under pressure, we wouldn't have the liquid nirvana known as espresso.

I say give it a try and let us know your results.