Back to the original question, I think that there would have to be several promotions as the draftees get signed. I suspect at least a few Ps would be/should be assigned to Beloit (Melotakis, Chargois, Duffy, Bard - when signed) a couple of the senior college OFs and BK Shanty or one of ST Cs would/could probably assigned there. So that would push for promotions up to Fort Myers all the way to Rochester (and some releases to make space.)
If I were one of JR Towles, Shawn Roof, Mark Dolenc, Clete Thomas, Nate Hanson, Aaron (the remaining) Thompson, Brendan Wise, Brett Jacobson, Matt Maloney, I would be dusting my resume at this point... and if I were Mike Holimon or Ray Chang, I would be doing some soul searching as well...
In addition to the previously mentioned Koch and Pinto who merit a promotion to (A+ and AA, respectively), Arcia (to AA), Herrmann (to AAA), Sano and Rosario to (A+), Deibinson Romero (to AAA) , Danny Santana and Jairo Perez (to AA), Drew Leachman or Nate Roberts or both (to A+). BJ Hermsen and Andrew Albers (to AAA), Dakota Watts (to AA), Tim Atherton, AJ Achter, David Hurlbut, Matt Thomson and Mike Tonkin (to A+) (pretty much the whole Beloit pen and being replaced by the new college signees) Matt Houser (to AA), Louis Perdomo (to AAA), Rickey Bowen and Danny Turpen (to AAA).
Something like that