if you are training to cage fight, or sport fight, better to train with them on. that way they feel natural and you get to know your limitations or abilities with them on.
though practicing without them can have you ready for the street in the event of a random fight, it all comes down to association. occasionally train in your street clothes and shoes for street application skills. you might be surprised at the difference. let us know how you get on, and any differences you encounter.