Technically yes but it is really hard. Rookie of the year winners get the pick plus the top 3 in the Cy Young and MVP races. The latter 2 categories are pre-arbitration so Crawford and Painter can get that for the next 3 years.
Realistically we are probably talking rookie of the year winners and pitchers only win about 26% of those so our best chance is Crawford winning ROY. I think his good year is hitting .300 and stealing 50 bases but hitting 9th his runs and RBIs will be down. All it takes is a Konnor Griffin hitting .270 with 20 HRs to look better in the eyes of the voters.
https://www.mlb.com/news/prospect-promotion-incentive-faq