Just had a guy drop from 56 to 36 WE as a result of not starting him even though I promised I would.

He's started probably 15 / 18 games.

If I start him the rest of the way, will the WE recover?

What did he start the season as? 

I think you've caught it early enough to get him back to at least what he started the year. I had that happen around 22 games (I think) and after starting the rest of the year, the player got back to what he started the season as, but he lost the gains he had made during the first 22 games (so it ended up costing him something like 6/7 WE points).