I've got a couple of friends who have stripped for a living and they are both sound. I really wouldn't worry about your mates recognising her, every time I've been lapping I have been totally wasted and probably wouldn't recognise the girls the next day if she served me breakfast. If they do recognise her it's because they are spending too much time at strip clubs and you could argue that's not healthy in itself!
Personally I might struggle though because I am fairly jealous, but if you can cope with that bit I would go for it. Like a lot of the other posts say, you will have a hot, confident girlfriend who won't be doing it for ever. Plus she will entertain you long after she has hung up her sequin g-string.
94 GT RTS 3 (in build)
05 Cinelli estrada
93 Saracen Ltd Edition - In need of love
93 Ozone O2 E-stay (the wife's)
2013 Whyte 129-S
2016 GT Grade