That's entirely possible.
The only reason we know I had COVID-19 is that, after a few days of what looked for all the world like an asthma exacerbation that was a bit more recalcitrant than usual (but nowhere near the worst I've seen, even in the last few years), I picked up an entirely-unrelated opportunistic bronchitis and coughed up a mouthful of green slime.
I've been under standing orders for decades: when that happens, see the doctor and get antibiotics started, before the bronchitis gets a chance to put me in the hospital. (It has happened.) So I went in. The doctor ordered the antibiotics, agreed that this was almost certainly an asthma flare, but insisted on swabbing me for COVID-19 anyway, since I am one of the patients considered to be at sky-high risk for a bad outcome *IF* I get COVID-19.
I emphasize at this point: I had NO symptoms, at any point, that clearly indicated a viral infection. No fever, no chills, no muscle aches and pains, NOTHING. The ONLY thing out of the ordinary was a funny taste in my mouth, and that could have been ANYTHING. I think we were both surprised a few days later when the test came back positive. (Interestingly enough, another COVID-19 test, taken the same day as the first, came back negative. The test depends on the swab actually catching something.)
If it hadn't been for the bronchitis, we would never have known I'd had COVID-19.