I've faced my own deck a few times now. A couple times I just surrendered if I had no rings lit and didn't worry about losing progress. Another time I played it out, and then gave up on the turn I was going to win. Just last night I lost to my own deck in another matchup with it.
If beating my own arena deck were to give me a rare spin, I'd do it. Otherwise I'd probably surrender or quit if I was about to win, unless it had no chance of making it to the top decks.