Actually, more megapixels
might help, by making the noise smaller over the picture overall, but it can be offset by how the noise performance is affected by the pixel density, so the short answer is "maybe, maybe not."
However, aside from simply the high iso setting, the other big culprit of noise is
underexposure. So, one technique to try to reduce noise is digital pull-processing. Checking that you don't run off the end of your histogram with blown highlights, expose slightly more than you normally would while shooting RAW. Then, in post, adjust the exposure back down. You should have less noise in the shadows that way. Another digital technique that's similar to HDR for accomplishing this is
Guillermo Luijk's Zero Noise.
More traditionally, you can also just use noise reduction software, like Neat Image or Noise Ninja.