I recorded a Classic RTA video without sound because SLOBS messed up my settings after an update and I forgot to check them.

Is it ok to submit the video or can I use a background music so it's not boring to watch it?

Nah, you're perfectly fine to submit the run.

sometimes my videos dont have audio because of copyright on music used in the background at times. (lol)

I personally wouldn't use Background music, or you might end up with copyright claims out the butt.

Even with royalty free music.

My intention was to use a fan remix of a Star Fox song but I decided to leave the video as it is.

No worries, just pointing out. I've had DCMA 'strikes' against me for shit that wasn't even playing, due to sound effects.

DCMA auto bots are not great.