I have some experience working with medical and patient handling programs, but no experience with SSD's.
That being the case I'd still feel comfortable in saying a tentative "no".
It really depends too much on the software handling the patient lookup (SQL database, Pervasive database, others, etc), and the machine hosting the database application.
If the doctor has a dedicated server running the apps and databases, then that could potentially benefit hugely from the SSD, especially as the data normally is of a manageable size.
The client application (the software the doctor is using for handling patient data) has to go consult the server and then respond with the correct info for the specific patient, and the application will not be speeded in any meaningful way by the SSD.
That being said, there can be very specific applications or programs running locally (diagnostics machinery for lungs, cardio, etc) which would have a very low chance of being speeded by an SSD, normally they are more memory and CPU intensive and less I/O and throughput heavy.
That's my cents