I would absolutely ask the owner first, but if it didn't come up during the meet and greet and the stay has already started, it doesn't hurt to ask! My first time house sitting I forgot to ask if my boyfriend could come over for occasional meals, but texted the owners after they had left. They were totally fine with it because we had talked about him during the M&G (where I live, who I live with, where he works, etc.) However I made it clear that I understood if they weren't okay with it too, so they didn't feel like I was taking advantage.
If the owners aren't okay with it, or if you don't feel comfortable asking once the stay has already started, use this as a learning lesson. You can go out to meals with your fiance, or go home for a few hours each day to spend quality time. And next time bring it up during the meet and greet, or even during the initial message so that they can meet your fiance!