Yes, that is possible, but it might depend on your audio interface.

Most sequencer programs like DP, PT, Logic, etc. give you the ability to "punch in" and "punch out"

For example, I have a MOTU 896 firewire interface hooked up to my Mac. The 896 has a 1/4" footswitch jack for a simple A/B footswitch. Using the settings in my Sequencer program (Digital Performer), the first time I hit the footswitch, the sequencer begins recording. The second time I hit the footswitch, the sequencer stops, rewinds to the beginning, and is ready for another take

This setup really helps when I'm recording alone, as I can use the length of the Firewire cable, and put myself, the audio box, a mic and headphones in a separate room from my Mac, thus avoiding the CPU fan noise. The footswitch allows me to record multiple takes without having to be at the computer.

As far as MIDI goes, I'm a novice myself :)

Whoops. Misread your question ... though the above technique is nifty. :D

I think the answer to your question relies on two things:

1) Which sequencer are you using? Almost all have a way to "slave" to an external clock for starting and stopping.
2) Can the Boss pedal send the control signal your sequencer requires?

My guess is that answer to the question will most likely be found in the Boss pedal manual: See what it can send, then see if that works for your sequencer.

OK so far that makes sense, but what am I looking for that the Boss can send? By the way I'm using Sonar with a Delta 1010. Thanks for all your help!