Yes, of course. First hand experience:
Was on a road trip out west in 2012. Got a cold on the way out there driving west. By the time I got to Cody WY, I got stuffed up, developed a fever, and lost taste and smell for 24 hours. It lasted another couple of days feeling feverish but not a high fever, took some Advil, then it went slowly away with a lot of coughing and spitting out crap. I had gotten to Yellowstone by then, stayed at a cabin in the park, and slept the whole afternoon till the next morning. Just got up to go eat something at the restaurant there, and back to bed. Taste and smell had returned, but fever was still present.
Never had a cold that caused loss of taste and smell. I'd say this thing may have just taken time to materialize into the covid variant that has plagued us up for two years now. No one had paid attention until people started dying. Till then it was just a bad cold for those who got it. Who knows? We may never know the answer, but I know I had something like it 10 years ago.