Most/all of the control towers in my area have radar displays, and I know from visits that it shows all the same things as in TRACON miles away--even aircraft on the ground. I hear them occasionally tell both VFR and IFR folks to reset incorrect codes, so they're clearly looking at (and presumably using) the radar display, even in VMC.
So why don't they say "radar contact" like TRACON does? It seems a little odd that you get a squawk from Clearance Delivery, and Tower checks the literal radar contact on their screen to make sure you got it right, but then you don't hear "radar contact" until talking to Departure.
Also, some busy airports will assign squawk codes to inbound VFR aircraft coming in directly rather than via Approach, but they don't say "radar contact" then either. This seems even weirder since in that case nobody else ever will--yet you're obviously a radar contact on their screen, otherwise what was the point of giving you the code?