A thorough read through of the excellent wikipedia article on the history of enigma cracking does give quite a few times the rotor wirings were deduced without any direct knowledge.
Most of these exploited the operational flaw where the same three character key was transmitted twice at the beginning of each message, giving insight into correlation between letters at fixed intervals apart. Over time, you could compile these small clues and make some assumptions. Given that the same 3 wheels were used for an entire day, you can learn a lot about the rightmost wheel over the course of the day. Sometimes they had captured code sheets, so knew the wheels, but didn't know the wiring. This would certainly help deduce the wiring over time.
My favorite anecdote from that page is this one that describes pretty much exactly your scenario:
Mavis Lever, a member of Dilly Knox's team, recalled an occasion when there was an extraordinary message.
The one snag with Enigma of course is the fact that if you press A, you can get every other letter but A. I picked up this message and—one was so used to looking at things and making instant decisions—I thought: 'Something's gone. What has this chap done? There is not a single L in this message.'
My chap had been told to send out a dummy message and he had just had a fag [cigarette] and pressed the last key on the keyboard, the L. So that was the only letter that didn't come out. We had got the biggest crib we ever had, the encypherment was LLLL, right through the message and that gave us the new wiring for the wheel [rotor]. That's the sort of thing we were trained to do. Instinctively look for something that had gone wrong or someone who had done something silly and torn up the rule book.
So yes, new rotor wirings could be deduced, but practically at the time they relied on a combination of espionage, operational shortcomings, and ingenuity to solve such things.
