Good question! My general answer is always: try it out, house rules are great and the designer can't stop you! ;)
However, I do love overthinking things, so let's dig into it a bit more. The tokens encourage players to plan out their story beats: you have to let your character suffer setbacks and get into scrapes, in order to gain tokens you can spend to succeed later on.
So a shared token pool might not work if you wanted conflict between player characters, or to have one character resolve all their personal drama while another was still struggling, but it should be fine for what you've described, with just two players. Your idea makes total sense for telling stories where the characters are under pressure to keep together, and have to take risks to help each other succeed.
If both characters take a joint action, I'm inclined to say you should still only gain/spend one token in total, because it's only one story beat. I'd describe it as one character leading the action and the other assisting them.
(Although I'd probably choose to spend two tokens for the characters to coordinate on a badass final move to end the session if I was playing! I don't know if your downtime is going to be that dramatic.)
I think it should work well, as long as your fellow player is cool with it. Don't be afraid to make adjustments midway through if you find running the game this way limits your options.
Let me know how it goes!