Yes any light/heat will evaporate water. Will it evaporate it so fast your res will dry before you notice it? No. The plants respirating will evap it faster than the light.
What i need to do is go out of town for 3 weeks and was wondering if when i get back it will have all evaporated
yes it will be dry. what you need is a remote reservoir with a float valve to keep your hydo tank full.
Unless you have one helluva reservoir. Mine is 15gln and I'd be hesitant to leave it that long. Worse than that as the solution is used/evaporates it could change the ppm and ph for the worse.
On a side note, regardless of the water level being sufficient or not, the amount of growth in that time frame could be significant. Maybe as much as 3 ft depending on where they are at in terms of life cycle. Plan on adjusting your lights with a lot of backup space, or have someone able to check it out. That's a recipe for a fire. I went on a trip for 10 days, and when I got back the tops of the plants were actually touching the bulb (400 watt hps) Praise jeebus for not burning down my house.