Sure, you can. Please remember to use the hair dryer with cold air. If you use the hot air, which will keep the nail polish more fluid instead of solidifying it, since cold harden polish. Most importantly, please use the soft code air. The nail polish will be smudged with the strong air even though it is code air.
The same principle apply to ice water baths. Fill a mixing bowl with ice cubes and run cold water over the top of your nails before getting it painted. Once you finish painting, dip your nails in for around a minute. In this way, it will help solidify polish and protect against divots.