Short answer: yes, but barely and smartly. Long answer: here's everything you need to know about gym and cologne.
The Case Against
You're sweating. Everyone around you is sweating. Strong cologne in a gym is inconsiderate — people are breathing hard and cologne mixed with sweat is rarely pleasant. Most gym-goers agree: the less scent, the better.
The Case For (Barely)
One spray of something light and fresh on your chest (under your shirt) can make you feel more confident during a workout. The key words: ONE spray and UNDER your shirt. Nobody else should be able to detect it.
Best Options If You Must
Versace Pour Homme — Clean and subtle enough to survive sweat without becoming offensive.
L'eau D'Issey — So light it practically doesn't exist. The safest possible gym option.
The Real Move
Save your cologne for after the gym. Shower, apply your real fragrance, and go about your day smelling great. The gym is for working out, not smelling good.