Unfortunately yes, if you are on probation then you may in fact encounter some difficulty in obtaining a passport.
Alot depends on what exactly you are on supervised release for.
For example, drug related felony convictions and non-payment of child support cases tend to be the basis for an outright denial of a US passport application.
If you are not on probation for one of the above mentioned things, then there is a small chance that you could receive your passport. It has happened before.
However for the most part, in practice if it does comes up during processing that you are currently on supervised release, then unfortunately your request for a passport would be denied -- in which case you would have to wait until your supervised release has ended to re-apply, at which time you should have no problem obtaining the passport.
Keep in mind the terms of your probation most likely require that you not leave the country during the probation term -- you want to make sure not to violate the terms of your release so that you don't run into any legal trouble or face a more serious penalty than probation.
It's best to complete your probation sentence, adhering to all requirements, and avoid any potential violations that would cause you more difficulty.
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