When a user goes to the image picker in MKTO, instead of it opening up the standard MKTO image picker we would like to open the Bynder DAM picker. First, is this even possible
No, the UI is not extensible like this.
AFAIK, the Bynder integration used to consist of syncing their library to Marketo's library using the standard Asset API and scheduling campaigns using the standard Campaigns API. Have no idea well those parts worked, but Marketo is no longer listed as an integration at Integrate Bynder, which suggests it never really worked. (Rarely does an integration live up to 100% of its claims anyway, but if there aren't any claims, that's impressively honest.)