I for one would never buy an ARM based computer, because my work life runs on RedHat/CentOS designing chips for a living. When Synopsys, Cadence and others port their tools to an ARM processor then I'll think about switching.
The majority of Linux/Unix code is processor-independent - its been that way since the dawn of time (Thursday, 1 January 1970

) - look at the shedload of software that is available for the Raspberry Pi. There's a lot of interest in ARM in the server market and Red Hat already support ARM:
https://www.redhat.com/en/blog/red-hat-introduces-arm-server-support-red-hat-enterprise-linux - if there's enough interest in the software you are using it will get rebuilt for ARM (...and Linux software tends to be either FOSS so anybody can re-compile it or very, very expensive - in which case, complaints on a postcard to the publisher). The only problem would be if there are no Linux drivers for the new Apple hardware.
If throwing a switch to go from Intel to ARM is so easy, certainly throwing a switch to go from 32 bit to 64 bit would be just as easy...
I'll believe it when I see it. Why didn't all the 32-bit popular apps that didn't survive the 64-bit mandate just flip one little switch and recompile?
...but that pretty much
is the case for any modern software - the only problem is where the publisher no longer exists or is no longer actively supporting their software so there's nobody to "throw the switch" - and all of that software dies next September anyway.
Without jumping through hoops like x86 to A-Series emulation (which people should remember is theoretical at this point in time) the simple answer is no, no they will not.
You could do
x86 emulation on ARM in 1988. More seriously, Microsoft already have a modern implementation:
https://docs.microsoft.com/en-us/windows/uwp/porting/apps-on-arm-x86-emulation - they might even license it (its impossible to predict when MS and Apple are going to fight or co-operate). However, ~1988 the ARM 2/3 was
seriously faster than its contemporary Intel rivals so it had the "headroom" to run a usable x86 emulation. Today, the ARMs advantages are power consumption and customisability rather than raw speed so any transition can't depend so much on emulation.
Look, lets have some reality checks here.
1. These rumors
could just refer to the use of ARM-based subsystems in Macs - as is
already the case in the iMac Pro and the 2018 MBP.
2. If Apple lets their Intel Macs get hopelessly out-of-date and then suddenly drops them all overnight in favour of new ARM-based systems, cutting off people who use virtualisation or Intel-only software at the knees, then that is all kinds of stupid -
but that hasn't happened yet. A gradual transition - maybe starting with some sort of iPad/12" MacBook crossover to compete with PC 2-in-1 systems, with the 'pro' Intel Macs staying current for some years yet - makes a lot more sense.
3. If you're
primarily using Windows or Linux then I'm not sure what permutation of misconceptions would lead you to buy a new Mac today given the far wider choice and variety of Windows hardware - and if Apple continue on their current course then, come 2020 you're going to be in a
very small minority (...plus Apple and/or Microsoft could easily break Boot Camp and/or Linux - because security - on new hardware even if they stick with Intel).
4. Windows on ARM already exists and could well be big by 2020. It might not work on BootCamp (but then BootCamp might die in the future as Apple's architecture diverges further from the standard PC - which has already started with the iMP and MBP) but virtualisation ought to be possible (yes,
ARM can do that).
5. "Just flick a switch and re-compile" is optimistic - but far closer to reality than it was at at the last architecture change in 2005 (even then, a lot of Apps were very quickly ported). Many developers currently supporting MacOS already have, or are likely to be looking at, iOS versions, which means that making their core software ARM/Intel agnostic is already on the agenda. Hardware Abstracted OS-level frameworks - Metal, Grand Central Dispatch, Core Audio etc. are far more prevalent than in 2005. As noted before - if Adobe can port Photoshop CS to iPad then its not going to be a problem to support ARMintosh.
6. Then there's the shift to Web/Cloud Apps - certainly at the 12" macBook/iPad end of the market, people aren't nearly as tied to MS Office as they were in 2005.
7. Yes, the Mac Pro would be the tricky one - but since the Pro and the Mini haven't been upgraded since 2012/3 (the 2014 Mini was a downgrade) most actual Pro users have already left the building and if Apple
did release a 2020 Pro with an exotic gazillion-core ARM architecture that worked brilliantly as a FCPX/Logic "appliance" then at least it would be
interesting.
TLDNR: Apple could switch to ARM
sensibly, stupidly or
not at all.