Yes.

That is to say, there is almost certainly some of both in your image. After all, there are more dim stars in the sky than bright ones. The brighter we expose, the more stars will show up. Likewise, the brighter we amplify what our sensor captures, the more stars will show up. But noise will also be amplified by the same amount.

If you really stop and think about it: no matter what your exposure is, there will always be some (hopefully very dim) stars that are the same brightness as the read noise in your image. Unless you intentionally take a frame with camera motion or slight focus blur, so that the stars are blurred but the noise will continue to be sharp points, it's pretty hard to tell the difference. Defocusing only works so far, though, because if you defocus too much you just spread the light from the dimmest stars you capture at a particular exposure level so much that they do not register at all. Long enough exposure without any tracking movements never lies. If the stars are streaks, they're not noise. If the stars are streaked, anything that is still a point is noise.