If WotC now is as smart as they were when Ryan Dancey was in it, they won't worry about it too much. He and Russ go into that a bit in this interview, and it turns out that the reaction of the business to this happening was largely, "If you think you can make a profit re-packaging free product I suppose you're welcome to try, and it's no sweat off our back since you've basically just made a brand customer for us."
Note: Throughout this I use OGL and OGC to refer to such things as they currently exist and as we're familiar with them. Because, if WotC changes them...well, that's exactly what I'm saying.
It's actually less about the Basic Rules and more about the second part. Lets say WotC releases the Basic Rules, and nothing else, as 100% OGC. What happens then? Answer: People remake the PHB. The PHB isn't free product, but 9/10ths of it can be brought forward from 3e-era products, and the remaining 1/10th are mechanical and found in Basic. Put 'em together, and BAM, you've got the PHB as OGC and outside of WotC's control.
Look at it another way. Turn it around. What does an OGL product require? Answer: Identification of OGC content. We KNOW the PHB and Monster Manual have no such identification, so those books can NOT be the source of OGC. What does that leave? The Basic Rules, or an SRD. An SRD would be a duplication of the Basic Rules, except possibly less pretty and with more stuff. That makes no sense. That leaves the Basic Rules. And we're back to where we began.
This is actually a really interesting period for me, and hopefully for anyone interested in a D&D license. Without a license directing or channelling content creation, the 5e fan resources are arguably a pretty cool indication of what the fans are interested in creating. Note that much of it derives from the PHB, not Basic. A license that doesn't encompass the PHB isn't going to be satisfactory.
There's a weird binary perception that WotC must use either the Open Game License or no license whatsoever, which is a completely bizarre thing to believe. Paizo in this regard is not WotC. Paizo. does. not. have. a. choice. I think Paizo is an awesome company, and I love what they do, but they're in bed with the OGL whether they will or nay. Credit to them for embracing it and this analogy is getting creepy so I'm dropping it, but we're talking degrees of acceptance, not negation. WotC isn't locked in like that. They've made one stab at a non-OGL license with the GSL. There is absolutely nothing stopping them from making another. The GSL didn't fail because it wasn't the OGL; it failed because it sucked on its own merits.
I think there will be a license. I do not think it will be the OGL. It's entirely possible that WotC might invoke some kind of non-commercial fan license. Or some kind of electronic-product only license. Yes, companies are still capable of creating work-arounds via the OGL, but either of those would satisfy 50-90% of the audience that actually cares and correspondingly cut down on the number of people who
need a work-around. You're not likely to get many first-tier game companies interested in that sort of thing either. No AEG, no Green Ronin, no Paizo, no Fantasy Flight or White Wolf. Whatever the license, it'll need to address material in the PHB as well as the Basic Rules, and future material, with a minimum of effort on WotC's part, and just slapping the OGL on the Basic pdf won't do that. WotC has been pretty damned careful with 5e so far; I think they'll put a similar amount of thought into the license.