Can I reassign the piano pedals to the volume controller?

Only if one of those pedals is a "half-damper" pedal that outputs continuous MIDI CC messages as would a modwheel. You can check for yourself: slowly depress the pedal and see if you get a continuous stream of data showing up in the transport's MIDI monitor section. If you all you see is one event (CC#64, value = 127) then the answer to your question is "no".

Suggest that if you're going to need this facility a lot then consider getting another controller that at least has some sliders on it.

Yeah, it's rare that you'll find a half damper, but it was a shot in the dark.

You can, of course, draw in volume automation (hyperdraw, right on the region) or ride the volume in real-time to track automation with mouse, right on the screen. Just enable automation on the track (Touch) and ride in your volume changes with the mouse.

I just saw your post on Logic Pro Help and posted something for you based on your reply to David over there. I'm not sure how practical it is, but that's for you to decide.