I was reading a thread once where they were talking about why the Ellimist didn't make Tobias a morph capable Human again. Someone asked the question "How would that not have blown his cover?", as if to say that it would definitely have done so. I don't remember if anyone answered the question, or who asked, or where the thread is. But I can't imagine it blowing his cover at all.
Yes, he'd be a homeless Human, likely living with Ax like Marco does later in the series. There are people who would recognise him, but the "I'm a runaway" story should stick pretty well. I don't see a big security risk in that.
So the question is, that if Tobais was made a Human with morphing power instead of a Hawk with morphing power, how might that blow his/their cover?