If I replace my nylon strings with steel strings on my guitar, will the neck straighten out?

I have an Acoustic-Electric Fender. I'm a mariachi musician, so after
about a month of having it I replaced the steel strings it came with
nylon strings. About 2 months ago, I noticed a lot of buzzing, and
eventually they just buzzed with no pitch.

When I took it to Guitar Center, I was told that was due to the fact
that I put nylon strings. Apparently, the guitar was made to have a
certain amount of tension. Since nylon strings didn't create as much
tension, the neck began to slowly tilt back.

In desperation, I come here to ask the following: if I immediately put
steel strings so it has the correct tension, will the neck tilt
forward as it originally was and get at least somewhat fixed? I don't
wanna waste $60 on fixing it.

I'm not an expert guitar player and it's not my primary instrument, so
if it'll at least make the frets create a pitch and buzz a little it
would be good. As it is now, it's just pure buzzing and no pitch.