Im gona go all negative on this one because I think the risks and cons heavily out weigh the possitive's. I mean unless youre sure that everytime this girl is in the gym at the same time as you, she will come over briefly say hi, give you a kiss ( and maybe motivating a smack on the bum

) and then go off to the womens area and stay the f*ck there, I wouldnt risk having a bad day or week... etc
Im sure the tired, worn out fatiged, tomato red faced look is not very attractive to a new girlfriend. At some point they are bound to be doing a little circuit on the machines... just over there you know... on the another edge of the gym in plain sight of where you happen to be working, she's gona watch you, especially when youre not wanting to be watched. Trust me, a girl will wait for you to finnish your last set on the leg press, last rep and out of breath recovery with your gym bud who loves to take the piss when youre all mashed and ask you complicated questions and laugh at you - just when you think a little respect would be due to let you off - SHE WILL BE WATCHING.
Besides every gym Ive been in, all the girls really worth having are already hooked up. The girls that look good and confident look that way because they dont give a sh*t that you exist, they may check to see if you are watching them, but in reality they dont need you, they already have their night in shining armour somewhere else.
And answer this question:
How many guy's have you seen training in the gym, who's girlfriends are there aswell, and are just 100% relaxed, focused and happy about it?