It would be wise to anticipate that, yes, you'll need to buy BOTH a PC and PS4 license. I will be surprised (albiet pleasantly surprised) if they allow players who play on multiple platforms to upgrade them all at once with one license.

Brightshadow has the right idea of what you can expect to see. You can play on the un-upgraded platform and still retain all levels, equipment, jobs, etc that you picked up in the new areas. The only thing you will not be able to do is enter expansion areas - and if you happened to log out in an expansion area, you won't be able to log in at all on that character on an un-upgraded platform.

I played FFXI on both PS2 and PC. The Seekers of Adoulin expansion was released for PC only outside of Japan (which is the only place to have gotten a PS2 release for that expansion). So, when playing on PC (expansion included), I was able to unlock jobs, earn equipment and so on and so forth in the new areas, and I could use all this stuff even while playing on PS2 (no expansion). If I logged out in an Adoulin area, though, I could not log in on PS2 until I moved my character to a non-Adoulin area.