TC, the plywood floor in the basement is 3/4" thick. And under the plywood is normally your black or grey tanks. I would not use any hardware that might take a chance of puncturing these.
Now some models might not have these tanks located there and you might get lucky and miss them with a 1 1/2" screw. There are some models that already have these drawers so maybe someone with them will tell you what size screws to use.