No, you can't do regex with processing rules. With processing rules you can only concatenate values, not parse them out. If you're looking to use regex to pull out individual values, you can do that using classifications. Right now you will need to use the legacy classification rule builder to do so until they add rule building to the new classification sets.
I'm not an expert in regex, but you should be able to write an expression that has a multi-character delimiter, and then in the classification rule builder indicate which value (1st, 2nd, 3rd, etc) that you want to return.