It doesn't matter how inexpensive Intel makes their GPU if it sucks and consumers don't want to buy it. If a manufacturer won't sell me the product I want, I'll go find someone who will.
Companies dumping GPUs are going to run afoul of government regulations really damn quick. This also assumes they'd give them away for free to begin with which seems pretty unlikely. Companies are in business to make money, not give people free products.
If Intel makes a "good enough" GPU and prices it well, it won't matter. They'll pull a lot of buyers away from the low end of AMD and Nvidia's market quickly, especially with OEM deals. Don't underestimate the subversiveness of large corporations to get their way. Nvidia and AMD are little fish to Intel. Intel will dump GPUs if they want to, not if the government lets them. Period.
(As an aside, if the government really cared about anti-competitive practices, it would have shown by now. But the re-merger of the baby Bells back into another giant AT&T, and the merger of Bell Atlantic and NYNEX into Verizon, shows that in reality, AT&T just wasn't paying politicians enough back in 1984.
I mean, just in the media industry:
Comcast owns NBC, Universal Pictures, Dreamworks, etc.
Disney owns ABC, ESPN, Nat Geo, 20th Century Fox, Lucasfilm, Pixar
AT&T owns HBO, TBS, TNT, CNN, Warner Bros Pictures, DC Comics, DirecTV
Fox owns, well, Fox stuff, except 20th Century Fox
CBS owns Showtime, Viacom, MTV, Nick, Paramount, Comedy Central
Sony-BMG merger
Add in Dow-DuPont, Heinz-Kraft, Charter-Time Warner Cable, Bristol-Myers Squib-Celgene, CVS-Aetna, Cigna-ExpressScripts, etc - and it's clear that there is no anti-monopolistic regulation. Intel will do as they please, because they put their money where the regulations are formed and enforced.)