Yes, it totally can.

I have severe tinnitus. First, I had a minor variant for many years. But what I didn't realize is that I was slowly losing my hearing in one side. Then I had surgery (tympanomastoidectomy) to remove the cyst that grew to the point it dissolved my stapes altogether, and now I have a severe variant, and significantly less hearing in that side. My tinnitus ramped up to a whole new level after that surgery.

I tried a phone app where you would play a tone that approximates the current tinnitus tone, or white noise lacking just that frequency area. In every case, all it would do is change the tone my tinnitus was making. Sometimes it made it worse than it ever gets on its own.

Likewise, in the summertime my tinnitus is regularly set off by the sound of cicadas. That tinnitus sounds so similar that at times I have to do an ear-plug test to see if it is just cicadas, or if is just in my head. No joke! I hate it big time.

Having said that, I now wear hearing aids (including for my ear that wasn't operated on, just to round out the age-related hearing loss), and this surprisingly makes it WAY more manageable. When I've been wearing them, I still always have tinnitus, but it is relegated to background noise. When I don't wear them for a long time, I'm usually punished for it. It takes days of proper hearing before the tinnitus goes back to background noise level sometimes.

BTW: I also get other types of tinnitus, which makes it worse. For example, on waking it is a really low sound that sounds like an idling diesel motor. I can even feel that one. I got that really bad after surgery, and I get it now when I'm ill. All of this was really debilitating for a couple years post-surgery, but I've come to grips with it now.

Just about anything can set it off. Cicadas, as I mentioned, but also rapid temperature changes, exertion (although weirdly I never notice it at the gym. It's just noisy enough there to mask the squealing I guess.), hearing something unexpected at a really high pitch, and being tired pretty much guarantee a hell of a racket in my head.