For most dentists to get Admitting and other privileges at a hospital, they have to be credentialed by that hospital. The credentialing procedure can be very long and tedious and full of red-tape. To get the privileges you have to show proof and record of your degrees, transcripts,training-specifics, GPR certificates, obtain letters from residency directors... You have to submit patient care records (i.e. hospital consults, Operating Room and Procedure Log Books, OP reports, Admit H & P's, Discharge Summaries etc).
There are general dentists on staff (often courtesy staff) with very limited privileges, and at times there are even general dentists who have greater privileges which include Admitting/Discharging/Operating Room/ Consult/ and writing Orders.
It all depends where you end up, what hospital politics are involved and what level of training you have. There are general dentists who have done OMFS internships or very strong GPR's and completed the History and Physical Course with the other residents and medical students... That's one of the essential needs to be able to admit and discharge.
Bottom line is this though. If you need to be treating a patient in the hospital, they are probably too sick/medically compromised and you are best to have a Hospitalist or Internal Medicine doctor on-board to manage their medications, fluids, electrolytes etc... Stick to doing the dentistry. There is no glory in having to manage all those headaches and complications. Your patients won't think any less of you...