Can this word be used to mean observing the patient's condition in a hospital in order to make a diagnosis?
It is a perfectly legitimate word to use. It is extremely common to say that the patient is to be kept under surveillance. The commonest use is in the context of patients with precancerous conditions who are routinely kept under surveillance for signs of malignant change.
'Observation' is my preferred term. We normally talk of a patient being kept in hospital 'under observation'.
'Surveillance' is not unheard of, but it has a sinister ring about it, and is used in connection with the police and security services, as well as 'CCTV surveillance'! For that reason I would avoid its use in a medical context.