in the good old days, a turn of 30 degrees off track would solve that problem.
Sod's law would dictate that your pressurisation failure hit you as you were over the New York/ Boston area - 30 degrees left or right ain't gonna help! As you drop your descent will likely trigger TCAS TAs and RAs so now there will be several other aircraft roller-coastering up and down, doubtless triggering further TCAS advisories in yet more aircraft. Would the TCAS systems in the various aircraft be able to coordinate their advisories with multiple conflicts?
Would it not be better to try to get a clearance before you plummet? Or at least announce what you are about to do and wait a few seconds for ATC to acknowledge? Mild hypoxia amongst a few pax is surely a price worth paying to avoid a you-know-what?