I inadvertently did this - told my boss I was leaving, and she tried to match my new offer. but I think her counter was motivated by the total surprise/unexpectedness of my leaving. I told no one during the entire/lengthy interview process, and I only told my boss once I had a contract/offer in hand.

between the raise and better benefits offered by the new company, it was an easy choice. but it was impressive & surprising that my old job tried to counter (& it wouldn’t have hurt my relationship or dynamic if I accepted their counter and stayed, so you could definitely try!) personally, I just needed & wanted to move