Definately it could happen, and does happen. I don't see why there would be any repercussions? You're likely to get a very small pony, very likely rideable size.
Of course, it can often be difficult for little studs to breed bigger mares but you always have AI, and where there is a will, there is a way! Mares have been known to actually lay down for small studs because they "want it" just as bad as the studs when they're in heat!
I'll post a pic later of Piksun, he was sired by a tiny Welsh Section A pony and his dam is a huge Oldenburg. Haha, they actually made a "ramp" for the stud and he bred her just fine! The little foal was adorable, and actually grew to bigger then pony height I believe.
Just look at a Caspian, and you pretty much have exactly what a Mini X Arabian is likely to look like. I wouldn't be surprised if that's how the breed itself actually originated, I can't remember now but I don't think so. But they're basically tiny little Arabians in appearance.
Ah, found the picture of Piksun! His sire couldn't have been much taller then 12hh and his dam was close to 17hh!
There's a lady on this board that has a TB/mini cross that is quite proportioned and handsome. I can't think of their name off the top of my head though.
That's me! *raises hand*. This is Thumper. He's pretty much the outcome . I'm pretty sure that a horse bred to a mini would involve frozen semen? I'm not all that well-versed on breeding, so I'm not sure about the exact terms, but probably not a live breeding.