Well, in a sense, yeah if you want the car to run correct then you need the o2's back on.
Without them the computer goes to a fixed setting and you will lose part throttle power, driveability, and gas mileage to name a few.
Realistically if they are the originals you should go ahead and get some new ones in there. If not then basically all of the power you hoped to gain by going to the longtubes will be wasted by not having a fresh tune.
Computer will default to a "limp home" setting. It will be extrememly rich and you'll be changing plugs on a regular basis. Drivability will suck, idle will suck, it will surge and die often. Have I talked you into putting them back on yet?
Why would you want to leave them off in the first place?
I had a 90 LX 5.0 that did not have O2 sensors. It used a lot of gas and the check engine light stayed on, but other than that, it did not have any major issues. I drove it like that for about a year until I finally took it to get it checked and they told me the problem. Of course, they would not fix it because it did not have any cats . But it did not have any of the other problems that you said (idling, dying, surging, etc).