Sort of
You could create an endpoint that is a wrapper for stored procedure(s) that takes the procedure name as a parameter, as well as the parameters for the procedure.
Once you have such a mechanism in place, you can create endpoints that expose procedures automagically.
http://yourserver/services/yourprocname?prm1=val,prm2=val,etc
If you feel really ambitious you can try out SQL 2016 and return JSON directly from those procedures. Then you can nest data using subqueries and return the JSON in a single payload. No serialization, no objects, just read the data and return it.
< 2016 you could put the results into a Dictionary and use NewtonSoft to serialize it. Assuming you are returning flat data you'd be good to go. Just use a reader and get the meta data from the column names for the key, and the value as object. NewtonSoft will convert that into JSON for you.
If you are returning hierarchical you could (by convention) create a series of runners that take the reader, and pump it into a Dictionary where object is another Dictionary Again the Newtonsoft stuff will help you out with the serialization.
Hope this helps, we are using this approach with 2016 and it is very nice to be able to create a stored procedure and call it without any middle tier code, deployment, etc. It just works.
Hope this helps.