Not really a good idea, especially if the surround wall is 'flimsey'. Even if you use silicone caulk, the bending and flexing will cause it to 'split' or even separate over time, and cause a leak. Unless you can find 2 locations in the surround that are butt-up against the wall.
If you want to hang wash clothes, rig something up from end-to-end, and NOT where the surround is part of the 'project'. DO keep in mind that you'll have some weight on whatever you rig up so finding 2 studs is VERY important. And to be sure of the 'location' of where you want to put the rig, have a shirt on a hanger in hand to 'hold in place' to see if works.
I've seen these Portable Clotheslines that you can 'stand' in your tub for what you want to do. It's just T-shaped piping that's hinged in the middle (for folding up) and with nylon rope between the ends. It works for me and there's no drilling required!
My best to ya and hope this helps.
Jay J -Moderator