I went right away to the DG MQ after riverwood, without starting vanilla MQ, so no dragons spawning and so on (it's easier if you don't have to avoid dragons). I'm at a point at which I have to look for the elder scrolls, and one of them is the one gotten through the main quest. I started Discerning the transmundane. Now, if I finish the quest and get the scroll, will I be able to proceed through the vanilla MQ as intended once I start it?

Yes

You mean, the quest elder knowledge will start and finish as intended, and only be much shorter, if I have the scroll in my inventory?