You will be fine! The signs in La Coruna were in Gallego, but they are close enough to Castellano to be able to understand. All shopkeepers and others spoke Castellano to us.
The only time we had a problem was when my husband wanted to photograph an old man in the neighborhood. I approached him and asked if we could take his picture. He began to speak Gallego. I explained that I didn't speak Gallego and did he know Castellano? He continued to talk, so we used sign language to show "photograph". He just kept talking and talking. My friend from this website said that he probably thought if he talked long enough, eventually we would "get it". It was quite amusing.
But seriously, you will be fine. English is not widely spoken in the North, but everyone will be able to speak Castellano to you.