In "The Principles of Aikido" Saotome Sensei says:
"Good ukemi training will allow you to see the future truly because your vision will be based on observation and intuition, rather than an arbitrary decision made in advance of the evidence. Good ukemi represents the same wisdom as that of the fisherman who through long experience can sense what the coming weather will be."
Training without ukemi is of course possible, but you aren't training in Aikido. You are simply practicing techniques used in Aikido. Aikido is much more than just a series of techniques.
I don't think that anyone trained solely as nage would be able to use Aikido in a real setting, nor be able to progress to the level of shodan. It would be interesting to see though.