Why do you think that would be unlikely?
One of the stated concerns MLB has with the existing MiLB structure is the wear and tear on players related to extended travel in some leagues. St. Paul is well outside the current MWL footprint and some of the closest existing MWL cities (those in Iowa and Beloit WI) are most likely to be among those 42 franchises at risk of contraction.
It's possible, I suppose, that the MWL could be broken up into 2 new Class A leagues, eliminating the worst of the travel to the eastern-most cities in the Ohio River Valley, but even Peoria and Kane County (Chicago suburbs) are a pretty good jaunt from St. Paul.
Triple-A teams are in a greater position to accommodate air travel.
The greater question, perhaps, is whether the current owners of the Saints would welcome the affiliation. They're apparently doing very well as an independent, choosing (and, of course, paying for) their own staff and players. Affiliate owners/front offices are not really involved with the baseball side of the business at all. They're event venue managers. Will the Saints ownership/FO welcome that? Would seem more likely that they'd agree to own a Triple-A affiliate than a low-A organization.
I'm a little surprised nobody in the media has asked them, yet. Maybe I missed it, though.