The OED doesn't explicitly say—at least not that I can see—that usages like "This movie sucks" descend from suck meaning "to practice fellatio." When a word has as many meanings as "suck" does, it can be difficult if not impossible to tell which came from which. You can't exactly go back in time and ask speakers or writers which particular meaning they intended, and you can only infer so much from context and relative timelines.
That said, the "fellatio" meaning seems to date to the early 20th century, while there are meanings like "to draw the goodness from" or "to rob of resources" that go back to to the 16th century. There's also a definition for the noun "suck" (sometimes "suck-in") meaning "a deception; a disappointing event or result" that dates to the mid-19th century and an expression of contempt "sucks to you!" that dates to the early 20th century. These all predate the "fellatio" sense, and they also seem more in line with the meaning of "this sucks."
In light of all that, I think it's possible or even likely that this meaning of "sucks" did not originate from the "fellatio" sense, though I think they became conflated at some point. Of course, later generations seem to have lost that association.
