Personally, I think its more embarrassing to be a city of 150 inches of snow a year but have no men's hockey team. Playing baseball during the standard college season, which this year ran from Feb 12, 2021 – Jun 30, 2021, has the potential to be a disaster for the first half of the season.
BC, for example, played a heavy road slate early but by mid March, they were playing a very heavy slate at home. It is often still snowing in Syracuse in March.
That being said, I understand that baseball is probably a more natural fit with the conference. I'd do hockey but they may go that way.