This idea is really playing with fire. I'll say how I'd do it if I had to, then critique OP idea.
-Free to everyone
-Limited to one faction*
-MP limited to Ranked only
Here is where you could diverge: (I'd go for both)
- Provide 3 SP missions from the campaign, they don't have to be in the original order. This acts as both tutorial and tease for campaign content.
And/Or - Provide one or two maps for SP skirmish play. Again you only get the same faction but you can play the same map as much as you want.
All this would have to be locked down tight so people couldn't add maps etc.
This involves more work, but it is both more limiting and more inclusive as a product, in good ways I think. It is more like a demo really and will likely take more work than the OP method but I think it would work a lot better.
* I first thought PHC was the obvious choice as they are easier to learn and are very/more popular. But if you take Sub missions from the new campaign they might be more interesting and can also be used to tell people how to play Sub. Also if PHC is more popular then it increases the likely hood they buy the main game so they can play them
Too generous, too narrow, shooting in the wrong direction:
Too generous: They can play all factions on all maps and all MP types. If players give keys to people who are only semi-interested in the game they will probably only play custom games with their friends anyway and so wouldn't buy the game.
Too narrow: Giving keys to friends won't work. I can't think of a single person (who doesn't already have it), who if I gave them the key they'd give it more than a quick go and only if I play with them. Unless I give it a few random people I don't personally know. I expect you would end up with keys just online, but that is messy.
Wrong direction: Your proposed way is aimed only at MP. You yourself have said vast majority of people only play SP. Those SP won't touch this and in their mind it might even create the idea that Ashes is all about the MP so it puts them off the game in the future too.
So none of them increase sales. And limiting it to keys for existing owners, well, I think you would get very little payback for the effort you put into creating Tournament.
I am not sure it is a good idea at all in the first place but the OP idea won't work well I think. One problem with free games is that people on the whole (I think) don't appreciate them so much and will often drop them quicker. It is the extension of the idea that if you buy a game for $60 then you will definitely play it and put some time into it. If you wait for a game for a couple of years and pick it up for $5-$10 in a Steam sale then the likelihood of it sitting there in your Library and barely played or even never played goes up substantially, in general.
Make Escalation as good as you possibly can and push it as best you can and see what happens. You can already play the game on pretty old hardware so apart from supporting lower resolutions better and continued general optimisations then I don't think you need to be creating a super ugly version for very low end users. With all settings at lowest the game doesn't look good as it is. Get Vulcan out there for Windows 7 users and then Linux. If you can get Vulcan support out at the same time as Escalation then you can get a free round of press from the tech sites comparing Vulcan to dx11 and dx12 performance You also need more start options, replays, better mod support/Steam workshop etc. As long as you keep working on the game and can get some press out when you launch Escalation and then 3rd faction expansion and then Navy etc., then people should keep getting the game and even the lower end gamers will have systems with 2GB of VRAM or more.
My main worry with Escalation and its reception would be some people buying the game and then refunding it just to put a complaint review that it is standalone. One good thing if you made the demo type I suggest is that hopefully people will try before they buy so you cut down on negative reviews of the main game from people the game doesn't suit.