Hi ocelot22,
To start, you should not be trying anything "new" on Test Day, so if you're curious about how a nicotine patch would impact your performance, then you should try using it on days that you take your practice CATs.
Beyond that, your profile shows 5 Scores. Are those Official GMAT Scores? Based on the 'swings' in those numbers, you likely have other factors to consider besides whether you use a nicotine patch or not. Before I can offer you any advice for your studies going forward, it would help if you could provide a bit more information on how you've been studying and your goals:
Studies:
1) On what dates did you take each of your Official GMATs?
2) How long have you studied in total?
3) What study materials have you used so far?
4) How have you scored on EACH of your CATs (including the Quant and Verbal Scaled Scores for EACH)?
Goals:
5) What is your goal score?
6) When are you planning to take the GMAT?
7) When are you planning to apply to Business School?
8) What Schools are you planning to apply to?
GMAT assassins aren't born, they're made,
Rich