Well, if you want to be mathematically correct (in an objective manner), the noise will be doubled. As niels nielsen mentioned doubling the power will yield a 3 dB increase. Now, whether this results in a doubling of loudness as a perception metric, then the answer is most probably no.
According to the book Communication Acoustics by Pulkki and Karjalainen and further references therein, as well as the very well known Equal Loudness contours (Wikipedia link) (also known as Fletcher & Munson curves), you can see that the perception of loudness is definitely frequency dependent. Not only that, but the dependence is also amplitude (or level) dependent!
In addition to that, the aforementioned curves are extracted from experiments made with pure tones. Due to some psychoacoustic phenomena such as the increase of perceived loudness when the spectrum covers more than one critical bandwidth (for more info refer to Communication Acoustics by Pulkki and Karjalainen or a book called Psychoacoustics - Facts and Models by Fastl and Zwicker, page 202) the loudness is also bandwidth dependent in a non-linear way.
It has been proposed in Psychoacoustics - Facts and Models book that, as a rule of thumb, a 10 dB increase in level (but this is for pressure not power) results in a doubling of loudness for a 1 KHz plane wave tone. As you can imagine by now, this is (as mentioned) a rule of thumb, since the phenomenon of subjective loudness perception is far more complex than this linear level-loudness proposal.
Finally, I apologize for not being able to provide more than just links to pages showing the book (and not the books themselves) and I hope I didn't complicate things too much.