I think if you put in the time and effort it could definitely be possible. I do want to give you a few things to consider, though. First, even if you are able to get your foot into the door, it may take additional training or certifications to land a job in their coding department. I would recommend you look into what their requirements are. Most hospitals want their inpatient coders to have AHIMA credentials such as RHIT, RHIA or CCS. These certifications also have eligibility requirements that must be met. See ahima.org for more information.
The second thing I want to mention is to please keep in mind that inpatient coders use ICD-10-PCS coding which is COMPLETELY different from how you'll learn to code taking a CPC course. I thought hospital coding was something I wanted to get into so I purchased the CIC course through AAPC. I quickly realized hospital coding is not for me. I do not enjoy it at all. I highly recommend you spend time looking into inpatient coding, maybe even job shadow a coder if you can find that opportunity. I'm not trying to steer you away from that type of coding, I just wanted to share my experience and thoughts on the subject.
Whatever your decision, I wish you the best of luck!