Depends on the type of fear and the degree.
Are we talking about an ongoing situation where fear is a constant?
I guess some students may be afraid of not getting it right, others of being hurt while some (judging by some forums on Aikiweb) are just plain afraid of other students. The latter two types, I suspect, end up quitting.
I liked Erik's reference to our invention of helmets. The 'butterflies in stomach' make us go on roller coasters and sky dive for no logical reason.
I'm not sure if I see Aikido in relation to the strong definition of 'fear' while learning though. I look forward to my classes (more a of a 'buzz' rather than 'fear') and have only felt actual fear or apprehension in one. I haven't been to that particular class since.
so my vote is 'no'.