When I came to Aikido, my karate experience helped me, well, not at all.
Really? My karate background helped me (and continues to help me) quite a bit.
I remember only one time in which we actually practiced falling in my karate classes; it was just not part of our curriculum. So when I came to aikido, I knew nothing about falling and rolling.
However, ukemi is far more than just falling. Some people say that the falling part is about 10% of ukemi and I tend to agree with them.
With my karate background, I have some notion of how to have power behind my attacks without being too off-balance. I have a feeling of what is open in my body during a certain movement and can react when these openings are taken. I have some knowledge of how my body moves and can move. I can use the same basic principles of deriving power through my body as I did in karate in aikido.
So for me, at least, karate has helped me in my aikido.