There may be good "cross-fertilization" but not as much as you might expect.
In the past many years, I have been to a number of Shuri-te dojos. And with rare exception, the approach that most take to bunkai could only be characterized as bad fighting. If you were to try some of these applications in a fight, you would likely get seriously hurt. There is a diversity of opinion as to how this sad state of affairs has come about, and in all likelihood, there are probably a number of factors. (But that would be another thread.)
Up until recently, it was difficult to make a convincing case for this, but systems have now published videotapes with both kata and bunkai, so there is official documentation of some of this really bad bunkai.
Goju Ryu, on the other hand, has a history of practicing good bunkai. Higaonna published his first tape in 1980, and more recently expanded on that with a series of videos. Chinen's tapes have been availble from Panther for many years as well.
So to answer your question, if a typical Shuri-te practitioner cross trains in Naha-te, then IMO, there will be some gain. But if a Naha-te student went to train in a typical Shuri-te system, then I am not sure what the gain would be.
I would recommend a different approach. If students want to learn better bunkai, have them study JuJutsu, Judo, or some other grappling art. To truly learn grappling, you need to spend a lot of time focused on the details of grappling. Once you gain the expertise, you are well positioned to figure out how to use these movements within the kata.
To me, the great beauty of kata, is that it combines block-kick-strike techniques with locks and takedowns. IMO, it is the combination of these two approaches that can open the doors to really meaningful interpretations of kata. You use karate blocks to protect yourself, kicks and strikes to temporarily stun, locks to bring vital targets into striking range to stun or further stun, and then throws to put the temporarily disoriented big guy on the ground where his relative advantage is mass is neutralized. And karate gives the best finishing techniques to the attacker on the ground, should your life depends on them.
One last caveat. There are exceptions to the bad bunkai rule. I have been in Matsubayashi dojos that taught good concepts, and I know of branches of Seibukan that do as well. There are others. Certainly Oyata has been a moving force, not only within his RyuTe, but also by teaching non-RyuTe students who have promoted many of his ideas to a broader audience. (I was first exposed to some of Oyata's teachings through Sensei Smaby, a Shotokan 6th dan under Nishiyama. And for all the oddities of his NTKOs and KOs in general, Dillman has published several books with some useful ideas.)
I also recognize that there are systems where good applications are kept tight to the vest, and only shared with those who spend many years training in the dojo. However, it has also been my experience that in many of these schools, there are often vast tracts of kata that are never addressed.
But this gets back to a different argument, and a different thread opened right now. "How many kata is too many kata?"