Hi, welcome to the forum! For me, yes, definitely. Whenever I get a cold or virus, my guts start acting up too. I haven't had a full-on flare triggered by a cold, and usually as I get over the cold/virus, my tummy starts calming down too. I'm not sure exactly why it happens, but it seems to happen every single time for me, so it's just something I've come to expect.
How severe are your gut symptoms so far? If it gets worse or doesn't get better after a few days, I would say call your GI and get their opinion. Hopefully it's just that your guts are a bit grumbly but will calm down again as you get over the cold. Get some rest, put a heating pad or hot water bottle on your tummy, eat mild foods like broth or rice, keep hydrated of course. Hopefully you will feel better very soon!