Depends on the teacher. I've seen teachers who demand their students to be a replica of themselves, and then I've seen teachers who allow their students to express themselves as "who they are."
One thing to note is that if you take a look at the uchi deshi that Morihei Ueshiba sensei had, they're all pretty different...
I think it also depends on the student. I've been getting out quite a bit lately (if you are in the Bay Area be afraid, very afraid) and when people find out where I practice (always the first question) "jiu waza land" (my sarcasm but it's close to what people imply or I interpret them to imply) I'm often told by people that they want answers. People say they want to know how
to do it. Or they just look at me like I'm crazy to hang out where I do--maybe they are the smart ones. I don't know if that extends to how to be
but it seems possible to me.
I would agree that you will mimic on some level. I've used this phrase (paraphased) before and I like it. R. Bolles says "maybe you should have been an artist, craftsman, musician, but you've been wallowing with pigs for 20 years and pigs are your style". Do something a certain way for a long time and see if you can change--easily?