yes the o2 is a vital part of the whole fuel injection system. under WOT the o2 has no affect on anything, the EEC has a target AFR to attain under WOT/open loop mode which usually is richer than stoichiometric (14.6ish AFR) usually its in the 12-13:1 range. for safety and max power. for a blower it needs to be even richer, the FMU takes care of this.
the o2 only works in closed loop mode, which is used at cruising speeds and idle (when the engine is up to temp etc etc, on a cold start the engine runs in OL)
anyways closed loop for economy and fuel milage, the o2 works in a narrow voltage range and either reads rich or lean, and the point where to o2 switches from rich to lean is stoichiometric AFR of 14.6-7. thats all the stock o2 is good for us reporting that AFR, the EEC adds or takes away fuel to achieve this AFR is closed loop.
so with no o2s, with the engine cold it should start up and warm up just fine ( in open loop), then when its up to temp the car should run like crap with no o2, its now in closed loop and the missing o2 isnt reporting back to the EEC, so the computer doesnt know whats going on and goes into limp mode and will probably make the car run rich.
so when up to temp idle and cuising around the car will probably not run as good but WOT shouldnt be affect at all and should run fine since WOT is open loop.
so if you want the best drivability and economy i would use the o2s.
i would also invest in a wideband o2, it its own sensor witha gauge reading the exact AFR at all times. so you know if the car is rich or lean and you know HOW MUCH it is rich or lean, a very useful tool and is almost a MUST on a blown car. you cant take chances, a blown engine is very touchy and one instance of the car running too lean will melt a piston in a hurry. forced induction isnt as forgiving as a naturally aspirated setup.
as for the t-stat, that will just make the car take forever to warm up and will stay in open loop longer. if you havent noticed a change without running o2s this is probably why, on a short drive the car probably doesnt get hot enough to even get into closed loop.