I'd do it IF the dryer is vented outside or there's an exhaust fan.
I put 2 large Golden Rods in my basement safe many years ago and haven't had any problems.
My unheated, un-AC'd basement stays damper than any little laundry closet. Okay, there is a hot water tank, gas boiler and insulated radiator pipes running along the ceiling, but trust me, it stays damp, even if there aren't always puddles on the floor when it rains really hard.
Summertime is really bad - cool brick walls, Richmond humidity.
I have a small, old house. My washer and gas dryer are down there too, but the dryer is vented outside.
John