I would think that obtaining a CNA would not prevent you from performing PCA duties at a hospital. In my view the CNA is a backward (downward) step from PCA(PCT). At least it is in my area.
If I were in your shoes I wouldn't bother with the CNA. If you're already hired at the hospital which provides PCA(PCT) training this work experience will likely qualify you for a position at another hospital if you were to loose your current PCA(PCT) hospital job.
But if you want to be overly cautious you could check if CNA is required at other hospitals. In my area it seems that the CNA is only required for working in nursing homes. Been there, done that, never again.
If you're looking for additional employable skills check for courses in phlebotomy (blood draw). These courses are about the same or less length of time as CNA classes.
From what I've heard, most CNA's working in nursing homes would love to be able to get a hospital job. So I'd say you got lucky getting the hospital job!
I've been working as a PCA at a hospital for a few years. My CNA card expired many years ago after I decided to leave nursing home work and pursue a non health care career. I had no problem getting my current job without the CNA certification. I was hired based on my experience from many years ago and my current desire to pursue a nursing career. I guess I was also lucky to get the hospital job!
Within the last couple of months I've applied online for PCA and critical care tech positions at two other hospitals. I received calls backs and interview offers for all the applications I made.
So again, if I were you, I'd concentrate on studies and the current PCA job. I'd go back to waitressing or ANYTHING else before I'd consider CNA nursing home work. Sure, I learned some useful and common sense things from the CNA course. BUT the work was tiring, hard labor, and back breaking.
Hats off to all you guys n gals that do that work and still have the energy for studies and classes!