Does the "deploy or get out" implementations regarding permanent profiles with a PULHES code of 112111 mean separation for those soldiers?

I think you just answered your own question - still deployable.
The way the process works is that you receive a permanent profile with a 3 PULHES. If you are still capable of deploying you will he retained and either medically reclassed or retained in your MOS. If you are incapable of deploying you will be med boarded.
It's not a new program and it follows the previous policies. It's just that now there is more emphasis for commanders to follow through with med boards of Soldiers instead of leaving a soldier to string together temporary profiles for a year or longer.

The "deploy or get out" is mainly for those that have been on long term profiles and are deemed non-deployable.

The function of is Soldier is to be able to deploy at moments notice. If a profile such as P2 precludes a Soldier from deployment or to do his/her job effectively, the Commander could request that the Soldier be reclassify into a different MOS that will allow the Soldier to deploy or in some cases request separation of the Soldier due to readiness.