Oh my goodness, Do I have a story for you!
I honestly couldn't tell you if it was worth it to go inside, but I can tell you it is certainly worth it to go even when closed!
My travel mates and I were splitting up for the day, he was walking ridiculously early with some friends, and as it was early in the Camino I was still walking slow and not worth traveling with for most anyone. So, it was on this day that I ended up walking by myself! And I figured I'd do something nice before I ended the day at Puenta La Reina and go see the beautiful church I knew the boys would surely miss, and make the extra trek to Eunate.
I need to start my story by telling you that, at that time, we only had one bottle of sun block, and because I wasn't thinking, I let the boys take it with them in the early morning! Well, being a very silly newbie pilgrim, I figured that the late June sun wouldn't be so bad. So, I started out, and forgot about sunscreen. Around two I made it to the fork for Eunate, and decided to go through with my plan to walk to the church. In the heat of the day, my arm which faced the sun began to burn and I realized there was not a drop of shade on the road to Eunate, and I needed to hurry, because I still had the trip back and to Puenta La Reina.
When I finally made it to Eunate, I arrived as siesta, and I needed to get to Puenta La Reina that night so I couldn't stay and wait until it was over. I was sad at first, but I had the peaceful sort of experience with only two other people their at the church, I wandered the grounds in a solemn quiet and benefited from the trees shade. I ate a small lunch and said a prayer, and made the journey back to the main road and to Puenta La Reina.
After returning, I discovered I'd managed to give myself a 2nd degree burn on my left arm from constant unprotected sun exposure, which would leave a scar that has not yet fully disappeared. But every time I think of that day, I don't think of the burn or the pain, or the hot sun or the long lonely walk. I think of that beautiful Oasis, the green and the holy beautiful church far from the main road. It was my favorite detour, and by far a strong point on the trip. Even if it is closed, I'd recommend anyone to make the journey... just make sure to wear sun screen!