A recent report from Bloomberg (unfortunately behind a paywall) suggests that Apple is building it's own chips to reduce it's reliance on Intel by 2020. The speculation is of course that these chips will be ARM chips based on the technology currently used in the A-series chips that are found in iOS devices (as well as the iMac Pro and MacBook Pro with TouchBar — though it is not the primary processor in those machines). There's also been a lot of speculation that this hints at some kind of merge between iOS and macOS but I have a few thoughts on that.
I think it makes a lot of sense that Apple would take ARM based Macs seriously even without any significant changes to their platforms. I think the primary argument in this respect is one of performance. The A-series chips in iOS devices have outperformed the competition in Android devices for a number of years now. This could be for a number of reasons, but one of them is that the hardware is designed specifically for the software it will run (iOS) and doesn't have to perform well on other platforms. It's likely that if you could just pop an A-series chip inside a Galaxy phone you wouldn't see the same great performance. Taking Apple's ARM architecture and applying some variant of it to macOS, with optimisations specific to the platform, will likely produce similar performance benefits.
I just don't believe that Apple would make this move unless they were confident they could match, and surpass, Intel on performance when applied specifically to Macs running macOS.
I think this is particularly true when running in thermally constrained machines. iOS devices have severe thermal constraints; it's a tiny, pretty much entirely enclosed device with no active cooling. Apple make a non-iOS device that fits this description: the 12" MacBook. MacBooks in general have thermal constraints, just slightly more forgiving ones, and then if you add a little more margin you have the all-in-one iMac. Apple can build silicon tailored to the thermal constraints of the device, and ramp up their balance of performance and efficiency cores on each chip to suit the enclosure and demands of that particular machine. Building specific A-series like chips for specific Mac models so that not only is the silicon designed for the software environment it will host but also for the hardware environment it will serve. Apple could hit the sweet spot on both counts and deliver the energy efficiency of it's A-series chips to MacBooks at the same time.
I think that if and when these ARM Macs are announced they will be demonstrated to have a performance benefit against comparable-generation Intel silicon as well as battery life benefits for the MacBook line — and the greatest difference will be on the machine where both of those are of highest importance: the 12" MacBook.
That isn't to say that iOS and macOS won't converge to some degree. Operating Systems have layers, and the two platforms already share the same foundation. There's probably a great deal of development on the deeper levels of iOS that would bring benefits to macOS even if at the user interface and third-party application levels these changes are more or less invisible. I'm sure that there are numerous other advantages to the two platforms (and likely tvOS and watchOS) having at least some shared codebase.
I'm skeptical about the user interface layers ever converging significantly; and this is backed up by the existence of tvOS and watchOS which are both iOS under the hood.