I haven't tested it yet, because it isn't available yet. It starts May 27, which is now. When I log into Battle.net I don't see a free faction change link, and when I go into the normal faction change link, my paid account has no game time nor characters currently on Barth, so it's a little difficult for me to test.
If someone has a paid account and can level to 10 on Barth, then go into the faction change and see if it's free, that would confirm if they're doing it that way. In the case of free realm transfers though, it's a separate link to paid transfers.
You can see that there's a link for Character Transfer, and also a link for Free Character Migration. So far, no Free Faction Change or what ever they plan to call it. If it's a separate free link, then I am pretty sure F2P can use it. If it's part of the standard paid link, then it's going to be a bit more complicated, since we will need to know the character id number, and even then, no guarantees. I'd be much more confident of it working if there was a separate link.