That is a no no. It won't hurt your bulb at all, in fact it will run nice and cool. The problem is going to be that it will be raining from your ducting and hood. You can use outside air to reduce the air temp getting sucked into your ducting but don't directly plumb it.
I have a 8" flex duct that is connected to an outside window. I then cut it in half. In the summer when it's 50 outside I tape the duct together and it's not an issue, nice cool air. In the winter, when really cold air will cause condensation, I just clamp each end of the duct to a little piece of wood with about an 18" gap in between. So when the fan is running im taking some 70 degree basement air and some really cold air from the window duct. If I get condensation, I simply increase the distance or stick an old shirt in the inlet duct.
You have to play with it a bit but you do end up reducing room cooling costs. The magic temp with no condensate (with an 83 degree, 40% humidity flower room) is about 50.