Back in 2007 when the celica gts (2zz) was a thing, I had a friend bring his celica gts with a greddy supercharger in because the check engine light was always on. He was running the greddy emanage with bigger injectors. While it ran great at the top end, the low end had no tuning because the place that did the install did not "do" daily driver tunes.
This was all new to me of course, I had only been tuning 90s toyotas without the ability to have software competing with the obd2 factory computer.
He left the car with me and said make it work as a daily driver. I forget what injectors were on it, if I had to guess they were 370 or 440. I started playing with the software and took out fuel on the low end without touching the top end which had already been tuned. It dyoned 300 at the wheels before I touched it.
I was shocked that that an engine with such high compression could be daily driven boosted with no issue. I drove it around for a couple of weeks and it felt stock until you hit the gas. You would get near 10psi before you could get your foot stabbed all the way. The problem is that automatic tranny would get a little confused at some points. Also, the super rich boosted nature would not clean up well after you slow down. The OBD2 would pick up this rich condition after driving normal and attempt to lean out the mixture. After a couple of hours, it will throw a too rich code because it couldn't compensate.
In the software I made boost give a TPS WOT condition, so it would ignore the sensors. The problem with that is, the computer will downshift when it senses WOT on the celica GTS. This was a problem because when I hit boost, the tranny would downshift, and you would hit warp drive going faster than you want to. If the car was manual, this wouldn't have a been an issue.
In the end, with my lack of knowledge at the time, I ended up just making the ECU reset every time you started the engine. A better option is to feed the factory computer a lame o2 signal and tuning the software yourself. If it had an AEM system for example, you can have it do the tuning. He was happy, I was happy, and we settled on the fact that
To sum it up, you can boost no problem. There were zero issues with boost at 10psi and he drove the car for years after before we lost contact. So, if you choose to boost, just make sure you have the right computer. Do not be like the honda guys who throw a turbo on without any management and post that you are rebuilding the engine 3 weeks later.