Yes, you can control who is eligible by inactivating trash guys during the all-star break. The only tricky part is the Rookie team which 1- has to have at least 20 players activated at all times, and 2- does not have any off cycles during the all-star break
Aside from that, the eligibility limitations are:
-there is no way to know who will get it and who will not.
-minimum of 0, maximum of 5 per franchise per season
-anecdotally, teams with notoriously bad minor leagues do seem to get closer to 5 but I do not have data to back this up. The ones they get are bad so it does not really matter. I'm satisfied with 2, if I get 3 I'm very happy. Sometimes you get 0 and that sucks
-must be on Active Roster on the DITR cycle.
-Makeup correlates to how big the initial boost is, as well as who has the highest potential OVR ceiling
-must be 24 years old or younger. **Pro years can be up to 6 and is not a limitation
-must be Projected OVR 59 or lower. Due to fluctuations in ADV budget this is an estimate. Guys with "55 projected" may not actually be eligible, and guys with "60+ projected" may actually be eligible
-iirc the highest Current OVR prior to DITR that I've ever observed personally is 52, but I may have observed up to 55 on other teams
-certain attributes are always fixed (defensive arm strength, all of the yellows, bunting and push/pull, and pitching velocity and gb/fb), while certain attributes can boost wildly (range+glove+arm accuracy and also PC for catchers, contact+power+hitting splits+eye, baserunning IQ, stamina+control+pitching splits+P1 thru P5.)
-sometimes Starting pitchers/long relievers with 3 pitches are capable of adding a 4th pitch. This has only been recently observed and may have been recently added. It may also relate to a pitcher who had previously lost his 4th pitch and has now regained it. I suppose the logic also applies to P4/P5 but I have not observed it personally
-long pitchers with P ranges such as 65-50-20-40 sometimes get "rounded off" to 70-60-35-35 (secondary pitches can go upwards and/or downwards)
-Because of the nature of fixed/variable attributes, the best candidates are always the ones who are already high in fixed attributes and currently low in the variables. This is why catchers and relief pitchers benefit the most, it's because of the nature of their fixed attributes.
-always Promote at the end of the season so that they get a big jump to carry over to the next season.
Best ones I've gotten when controlling via active/inactive:
Player Profile: Derek Jenkins (80 OVR RP)
Player Profile: Fernando Colon (79 OVR RP and climbing)
Player Profile: Javier Guzman (73 OVR sicko defensive C with reasonable bat)
Player Profile: Damaso Castillo (career .785 OPS with career 2.77 catcher ERA)
Player Profile: Aneury Cabrera (74 OVR C, traded for ML pitching, having a .950 OPS season)
On the horizon:
Player Profile: Enrique Costilla (C with excessive defense and a decent hitting stroke)
Player Profile: Yordano Lorenzo (SS with allegedly 80 OVR potential, note the DITR boost of +16 vL and the Promotion boost of +6 more vL, and +14 eye and +4 eye with promotion boost. Need to bank those)
Player Profile: Pablo Ramirez (C with big promotion boosts)
Player Profile: Matthew Dubler (RP who could be good)
Player Profile: John Paul (RP who could be good)