Misiorowski - I can see a mid-season BP stint - similar to Burnes/Woodruff.
Quero - Initially, knock the rust off at AAA and be available if someone gets hurt. Wouldn't surprise me to see a late season call up with Contreras playing more DH and Quero/Haase doing the catching (assuming failures with other DH options here).
Black - I'm not as hopeful as others. I'll guess he bounces back and forth a few times.
Yoho - I think he will start at AAA, but be one of the early callups for the BP. Might be the most MLB ready of all the rookies we have.
Connor Thomas - Sounds like he will take a Bryce Wilson role in the BP. Rule 5 pick that has the rules in his favor to stay at the MLB level.
Gasser, Patrick, Henderson, Rodriguez - Will be the starter backup rotation. Gasser when healthy might have a chance at sticking in the starting lineup.
Durbin - Depends on what else happens this year. If no more INF are acquired, he might get first shot at the starting lineup to show off their new sparkly acquisition. If not, he is probably competing with Monasterio and Dunn for the utility role. Which probably means a bunch of time at AAA.
Boeve - could make a short stop at AAA if our 2B/3B options aren't doing well before coming to the MLB. But since he isn't on the 40-man, I'm guessing things have to go poorly before he is added this year.