It's not bad to have that as your "goal" or "end-goal", I'd say it's perfectly reasonable to accept that some degree of fame is, in a lot of ways, how many actors gauge their success. That said, the expectation of fame in the years following graduation is an extremely detrimental delusion to have.

Yeah, man! Drama school is amazing and it gives you the foundations to really explore roles to the deepest degree -- it'll make you ten times more versatile and just a better actor overall. Good luck!

I was on the three year BA. The first time I auditioned I was 17 and basically got laughed out the room [terrible choices of monologue], at 18 I spent some time with a rep company touring Europe, then I got an agent at 19 and started doing some professional work. At 21, I decided that I needed training, auditioned for the second time and got in... got pulled out when I was 24 for a small role in a TV show (plus a contract offer from a major agency). Hope that helps.