Yes. Last fall I got a cold for the first time in about six years. (I virtually never get sick in the common sense of the word.) During and after that cold my usual headaches and some other symptoms were dramatically improved.

My thinking at the time was that if there was any causal effect at all, it was that having the cold distracted me from the usual headaches, thereby reducing any psychological component they might have had. But who knows what other mechanisms could be at work?

I would think very carefully before trying to catch a cold, however.