Yeah, it has to have a dedicated expression pedal feature. Otherwise, you'd have nothing to plug the expression pedal into, and the pedal wouldn't "know" what to control.
A lot of Boss pedals can use expression pedals, but for those that don't... there's a world of similar effects in other brands that CAN use expression pedals (especially if you explore the boutique market).
There's also a product called the Tone In Progress (T.I.P.) Third Hand, which attaches to a normal pedal knob and allows you to move that particular knob with its special expression pedal. I'm not sure how well it works, as I've never used one... but it's the easiest solution for most pedals, since you don't have to do any modifications. This is as close as you'll get to what Oreomeister was joking about.
Regarding pitch shifters... there's the Digitech Whammy if you want a classic manually-adjustable pitch shift effect - it is pretty much the standard in manual pitch shifting. In terms of Boss... the PS-5 can control pitch shift sweeps by expression pedal, but it's limited in terms of what ranges are possible. The old Boss PS-3, however, is fully flexible in terms of setting the start and stop points for pitch shifting and harmonies.
For delay... there are a lot of boutique pedals that can do what you're looking for. Or, you can always stick the delay in a feedback loop pedal that has expression pedal capability (like the Barge Concepts VFB-X).
