A debug console can run any homebrew, multiman included, but you'll probably have to modify multiman to work on 3.70.
Also you can't just update to a debug firmware, coding has a thread on converting a retail ps3 to debug but it's currently missing one step, soon as it's known how to convert an EID0 dump to the idps file then you can boot debug on your console... Ofcourse your ps3 has to be on 3.55 to begin with to be able to do the steps