Another FLex Situation

[Dukat]

I have searched and did not find a situation like the one I am describing so I hope I did not miss it and am asking something that has already been discussed but here goes: Fed Rules

Say you have a player who is a good hitter but not very fast and not the Pitcher or Catcher so not able for a CR. Could the coach do the following:

Start the game with 10 players in the lineup and that player listed as Flex and someone else as DP.

Before the 1st AB of the game for the DB, go and tell the umpire that the FLEX is going to bat for the DP (DP Out of Game)

She gets a hit and is on 1st and then coach comes up and says she wants to reenter DP to run and move that player back to FLEX.

The question is, with a very deep lineup, could that coach continue to allow the Flex to bat every time up at that position just burning a new DP player each time she gets on base by subbing for the DP position and returning her to Flex after she gets on base?