Edit: My point in that scenario is that if she had gone through power testing first then she would lose her main protection from wards duties and would have to go through things such costumes and making an official debut.
No she would not, even then she could just stonewall, they would just have slightly more ability to punish her for it, but it's still not illegal for a minor to refuse to work, no matter if they have signed a contract, by US law, the ability to punish a minor for not living up to an employment contract, is limited to not paying them, so all they would be able to do, would be to dock her pay down to nothing.
Taylor saving grace and problem is that in this case is that she is trying to act within the margins of all laws and regulations since she believes is the only way she won't be screwed any worse by the powers that be. Is a plus to her since she is actually very good at finding loopholes and legal impediments to the Ward's regulations even on limited available literature (she made her initial plan based on little more than a pamphlet and an abridged rulebook literally for children and teens) and it has managed to hold against scrutiny from the PRT legal team. Its a long term problem because she is not a lawyer nor she got practical experience in burocracy, so far the PRT/Protectorate has been careful not to push their own loopholes too far to avoid alienating her even more but the fact is that if legal put some serious effort towards finding workarounds they can easily write pausible exceptions to many of the regulations that would hold up in court and frankly that would be also considered as common sense instead of something more sinister.
For an innocuous example take the mandatory Pizza Party Taylor managed to avoid by claiming that since it was a powers allowed activity it was too dangerous according to regs. Now if the director, or even the Ward's leader wants to really push the envelope they can start an activity known as No Powers Week, in which the parahuman Wards and Protectorate heroes would stop casual use of powers in their HQ as a show of solidarity with normal people, something that not even Youth Guard can complain about since it does help the peaceful integration of parahuman into society. Suddenly the expectation of the Pizza Party is that powers are not allowed so Taylor's complain is adressed as effectively as the HQ tour, but without being explicity targeted against her so no last minute YG save there.
The problem is, that they are not actually legally able to compel her to do anything, US law don't allow you to punish minors for not living up to employment contracts, and legal guardians are also limited in what punishment they can inflict on their wards, they can certainly make life less comfortable for her, but they can't throw her in Juvie or anything like that, the worst they can do is try to ground her.
The main reason why Taylor's plan has worked so well to this point is because Armstrong is not willing to poke her too much in regards to getting her integrated with the program, if she was with a different director such as Piggot or whoever she ended up with in canon you can bet they would have had legal on the issue from day one to find a loophole to force her to comply with the program, which would have ended in a runaway ward and ends up with either Taylor becoming a villain thus tarnishing the PRT and the Wards reputation, or Taylor being captured and put on probation thus losing what protections she does have.
Running away from home is not a crime in a majority of US states, so even if they captured her, unless her state is one of the minority where it is, running away wouldn't allow them to put her on probation.
Even in those states where it's technically illegal, the punishment only tend to amount to things like fines.
Of course there's always associated offenses, if Taylor is running away, then she's going to run into Truancy laws, and might run into Curfew laws if she's not careful, but neither of those carry serious punishment either, so they still wont allow them to put her on probation, because at most, even if they put pressure on the judge to apply maximal punishment, breaking those laws would get Taylor a few weeks in Juvie, and I think Taylor would take that over agreeing to probation.
And unless she's in one of the minority of states, that have running away from home itself being illegal, she can also just choose to continue going to school, and just use her power to get out of whatever grounding the PRT try to impose on her.