Well of course they would be the best of friends - enlightened beings of this supreme and ultimate level of attainment would have nothing to squabble about. We might imagine, that ultimately, in the Dharmakaya, the Dalai Lama and Dorje Shugden are also taking photographs together.
Remember also the famous story that the 16th Karmapa had manifested great disapproval at the fact that a Nyingma monastery had an image that depicted their protector stepping upon Dorje Shugden. And later, also acknowledged the rising prominence of Dorje Shugden in the world whereupon eventually, one day, said the Karmapa, "you will definitely need to rely on this deity."
Here's an old post by poster Vajraprotector:http://www.dorjeshugden.com/forum/index.php?topic=1809.msg25133#msg25133
While the Sixteenth Karmapa (the previous Karmapa) was on a pilgrimage in Nepal he stopped at Urgyen Rinpoche’s new monastery. At that time the Nepalese king and queen were there and came out to greet him with a scarf. When he went into the monastery there was a statue of Guru Dragpo with Dharmapala Shugden being pressed down under the statue’s feet. The Karmapa stood in the presence of the statue for awhile, then pointed his finger at it and asked “who is the person that said to build this statue? This isn’t Nyingma nor Sakya, certainly not Gelug and not Kagyu either. I didn’t say to build it, this is not one of the deities you can’t rely on.
Although the time is a little early in the future you will definitely need to rely on this deity.” Out of all the abbots and masters present not one came forward to answer. The Karmapa said “remove this now.” Immediately a person with an axe and shovel came and had to remove it. Many lamas present at that time definitely remember, a seventy five year old man from Chamdo called Samcho witnessed this event. - from Kyabje Dagom Rinpoche's sungbum