I'd guess even if they do build the Yonge extension without the DRL, then the unusability of the Yonge line afterward might get us the DRL a lot sooner than if we just sit and wait for them to build it first or at the same time.
That's probably the worst-case scenario that still involves getting the DRL (obviously the worst-case scenario period is that they ever only build the Yonge extension and the Yonge line south of Eglinton is screwed over for generations).
At the very least, I would hope that the DRL is shovel-ready when the Yonge extension opens. That way when it all plays out, and the Yonge line is overwhelmed, people riding it can at least say "ah, so THIS is why we're spending $4+ billion to build a new downtown subway!". If the DRL is shovel-ready by the time the Yonge extension opens, the Yonge extension will be the best ad campaign for the DRL there is. We just have to hope that we don't have to wait another decade until we get it.