00-02 should be fine - in theory you proceed as with 2zz swap: move the O2 sensor wires from the engine harness connector to the body harness connector and swap the TPS wires at the TPS connector. NOTE that the Celica uses only one upstream O2 sensor and it should be physically positioned downstream of the 4-to-1 exhaust merge. If you just plug in one of the upstream O2 sensors from one of the two stock MR2 locations then half the engine will remain unmonitored by the ECU. Look up 2zz swap wiring or such. You will have a minor issue with the P/S pump running all the time but maybe someone has discovered a wiring fix for that. To be entirely on the safe side you need to look up the pinouts or callouts for the Celica 1zz ECU and confirm it. Check newcelica.org maybe someone has posted it there.

PS. I just read through some very old threads on newcelica that confirm that the Celica 1zz and Celica 2zz have the exact same ECU wiring pinout - except for the three wires for lift. So this confirms that you can proceed with the wiring just as you do for a 2zz swap, which is very well documented in this forum: move the O2 sensor signal wire and ground terminals on the ECU connectors, and swap two of the TPS connector terminals - that's it.

 

Many of the SMT to manual swaps use the celica ECU instead of trying to re-key a manual MR2 ecu, so it can totally be done. You have to cut into the harness and move/cut/add a few wires to make it happen. There's a really good chance the MWR 2zz swap harness would work and it's plug and play, but you should do your homework on that.

Like Frank points out, you do inherit a few quirks with this change. The PS pump runs when the key is in the on position, versus only after the engine starts. Unless you change you exhaust, the O2 sensor will only sniff 2 cylinders which has it's own potential downsides. Both of these things are better than having a car that doesn't run.

Good luck!