Look at the ticket sales of Gopher FB vs the regional teams compared to other nonconf games vs lower tier opponents. No noticeable difference.
It's a lose/lose for the bball team too. Win = you were supposed to win, no one cares. Lose = you lost to a smaller school that you should beat, embarrassing.
I don't think it's really a like for like situation, but looking at wiki when NDSU came to town in 2006 they drew 62,000. Only game with a bigger crowd that year was Iowa. In 2007 the Bison game was the biggest draw of the year 63,000 and the only other game within 10,000 was the Badgers (59,000).
2009 the 1st year at TCF, SDSU is recorded as a sellout (as were all games that year).
2010 SD was actually the 3rd biggest crowd behind only USC and Iowa, though every game was within a couple of thousand of a sellout.
2011 NDSU was about in the middle for crowds, though pretty much every game was above 48,000. Actually sold a couple more thousand tix for that game than for Iowa.
2019 SDSU drew 49,000 which was 8,000 more than for the other non-conf game (Georgia So). To be fair, there was a big marketing push to sell that one out plus as the openers free tix for the incoming freshman students. Still it was the #3 crowd behind only Penn St and Wisconsin.
With that small sample size for football, it does make a difference. Plus for St Thomas there would be much less travel than any of the Dakotas, though I suspect it was also a lot of alums that already live in the Twin Cities that bumped the numbers.
In the grand scheme and extra 3000-5000 for a St Thomas/Minnesota isn't going to make or break the budget, but I don't think it would be insignificant. A few hundred grand at least.
As a Gopher fan but non-season ticket holder I usually go to a half dozen hoops games including a couple of non-conference games. I would be far more likely to try to make it to the first game they played each other if for nothing else the curiosity factor.
It would get a lot of media buzz.