I don't have a legal answer for you, but I can give you my experience. I had a restraining order placed against me after I asked for a pizza delivery girl by name when I ordered my pizza. Even better, SHE didn't place the restraining order, the restaurant did! lol So I couldn't get Papa John's for a year
(the girl found me later and said she had no clue what that was all about).
A year or two later, I went through the process of applying for a CHP without a hitch. I've also purchased multiple firearms since then. On top of all of that, it never showed up on the criminal background checks I've had recently. So, while I can't say for sure, I wouldn't be too worried about it causing you problems.