I have no idea if they can based on the rules and/or team philosophy but here are my thoughts just for fun.
I believe there are 6-7 wrestlers who have a legit shot to take home the title, and 2-3 more that could make it under the lights.
Garcia -- Although 126 is a meat grinder at Evansville (see post in State Rankings updated) he is at the top of the food chain and no reason to move.
Rooks -- Very capable of winning at 126 but CE does not have a ranked wrestler at 120 and he is the defending State Champ at that weight. It would shock me but if he could qualify for 120 he would become the favorite.
Viduya -- New Castle SS already has 7 ranked kids at 120, no reason to make it 8.
Egil -- EMD has state ranked kids at 106, 113, 120, 132, 138 so there is no movement in that lineup.
Poynter -- Portage has ranked wrestlers at 113 & 120 so dropping is not likely; 132 has 4 ranked kids at East Chicago so moving up would still present a realistic shot to advance to State.
Smiley -- He has already dropped from 132 and only him and Alec are ranked at 126 in New Castle; no reason to move.
Mills -- Brownsburg is similar to EMD in the fact they are loaded around him, no where to go.
Mejia -- Fort Wayne is weaker at 120 vs 126 (based on rankings) and the team does not have a ranked wrestler at 120 currently. Has a victory this year over the #1 ranked Watts.
Willis -- See notes on Mejia but substitute Evansville for Fort Wayne. Has a victory this year over the #3 ranked Fair.
Once again I have no idea if any of these wrestlers can move per the rules or if the team will allow it BUT if it was possible I only see it making sense for a few.