Is it wrong to hold a soldier back from the board if they are not developing themself (e.g. college, correspondence, cleanliness, etc.)?

SSG (Join to see) No... Only those Soldiers deemed ready by their chain of command should be sent to the a promotion board... assuming you are talking about E-5/6....

Heck no.
Just make sure you counsel them on ways that they can improve themselves in order to be recommended.
My personal qualifier is I want to see them train Soldiers. I feel that it is such an important part of their duties as an E-5, that not having done it should hold them back. Of course, the other side of the coin is to ensure that they get training opportunities, and that their FLL helps to ensure that they are prepared for training.

You said "cleanliness".
If a person can't keep themselves and their living space cleaner than my children do, you aren't holding them back, they just aren't ready.