I would imagine it would, I have a crappy Acer Aspire 5720z and it plays STO fine with most of the settings set to medium-high (this includes running on full resolution, although I do play in windowed mode)
I consider the graphics great compared to my last laptop and the framerates are usually very decent. I do notice lag on some of the busier maps but I'm more than happy with the performance considering everyone was telling me it wouldn't run at all.