The Carden House Traditional Kitchen, Austin

You can certainly do whatever you want, however I would ask why you would not want to go with an undermount....they are SO much easier in terms of cleaning your counters!
Nothing gets stuck under the lip of the sink, which can be annoying and difficult to keep clean, it just swooshes right into the sink!

I have never done a drop-in sink when clients go to granite or quartz counters, I always advise them (when they call me for advice on changing a countertop) to also budget for a new sink (undermount,) usually a new faucet (unless you like yours, in which case you can reuse it), and the labour for the plumber to disconnect and reconnect the plumbing (when a counter is being changed as opposed to a full kitchen remodel)

If budget is the issue, then you can always look for a floor model sink, or go to a big box store, as they can be found in all configurations/sizes, and often for less money, as they carry more of the budget-friendly brands. Try Kijiji or Craig's List as well, you may get lucky....all of this to say, even though you can do anything you please, I would strongly advise you to go with an undermount.

Undermount sinks do not cost much more than a drop in sink -- for future resale value, you should really go with the undermount.