I know people have had their work on display in galleries, though I believe in smaller galleries and nothing like an art museum. This seems to be a bit more common over in Europe than in the US. I think some painters like Roman Lappat have had their works on display. In the US, Matt DePietro did, but I'm not sure if anyone else has or has even tried. There are people like Alfonso Giraldes who are really pushing for miniature painting to be seen as an art form like regular painting, sculpture, etc. I don't think it's viewed like that yet by the more established art world, but in time it hopefully will be.
In short, I absolutely think mini painting is an art. You are creating something and expressing yourself. How 'good' a piece is doesn't matter. If you think of 2-D painting, a beginner/amateur isn't going to be very good, but it's still art. Of course, not at the level which would be shown in a gallery.
What I think miniature painting has trouble with is acceptance by the larger art world as another area of art. I think it's in part due to the relatively small community (plenty of people out there who know next to nothing about mini painting) and it's association with gaming. Easy to write it off as just toys and not art. But that again is related to a lack of experience. Anyone who looks at the top work in the gallery here or P&P would hardly call any of those toys.
Another issue which puts mini painting in a strange spot is that fact that most of us paint commercial kits. If you sculpt and paint your own piece, that's easy. Go to almost any art museum and you'll find painted sculptures. At the point it's just a difference in the scale. But I'm not aware of any parallels with the other more established areas of art for working with a commercial kit and building the art on top of that. In that respect, the more you change the kit (through conversion, through dioramas or scenic bases, making it convey a story or emotion), the more it's going to seem like art to people outside the mini painting community. I've described it in the past as somewhere between 'paint by numbers' and 'art.' When I just started out, I did flat painting, just following the sculpt (essentially paint by numbers, adding nothing new). As I improved, I began shading, working with light, adding texture, weathering, freehand, etc. I began putting more and more of my own take on the figure and pushing it towards art (or at least what a gallery might consider art). It's something I continue to work on.
So yes, mini painting is absolutely art. But what will it take for it to be accepted as art (and known more widely) by those not in the figure painting community?