Gear agreement?

[Somebody121]

In the Q and A I saw this answer relating to Gears that could happen to fall or roll from the an alliances loading lane to an opposing alliances station.

Q42: Is a human player allowed to feed a gear through the Overflow Loading Station?
If a GEAR were to inadvertently become displaced from a LOADING LANE into the opposite ALLIANCE'S ALLIANCE STATION, could that ALLIANCE'S HUMAN PLAYER use the overflow LOADING STATION to feed the GEAR onto the FIELD?
Answer: Yes, per 4.6 "GAME PIECES that roll, slide, or otherwise transfer from a LOADING LANE to an ALLIANCE STATION (or vice versa) are considered “owned” by the ALLIANCE in the space now occupied by the GAME PIECE."

I was thinking a new strategy could where both alliances take the 18 gears located in their loading lanes and move them across the line into the opposing alience station. This would allow both teams to reduce gear cycle times significantly. Do you think FIRST would allow this?