OSRIC was indeed out before 4e was announced, but that's completely different from saying that the OSR movement online had gathered a lot of steam and a high profile. That timing becomes a bit trickier, and it becomes more difficult to separate the announcement of 4e as a possible contributing variable. I heard about OSRIC for at least a year before I heard of the OSR acronym and discovered that there was an online "movement" associated with OSR, including other retroclones, new publications, a fairly active blogosphere, etc.
Although I obviously can't prove it, I suspect strongly that the migration to 4e by WotC greatly spurred the OSR movement like a shot of anabolic steroids. You're right that it can't be a cause of the movement existing at all, but I don't think anyone can claim that it wasn't a contributing factor to the growth of the movement into what it is today; people who were dissatisfied with the direction 4e was taking (according to previews of the edition) were turned off and went looking for something else, finding the OSR and realizing that their tastes really were along those lines all along after all, etc.. The question becomes one of degree, and how much did it contribute, but in my opinion, it's not a question of did it contribute. I think the answer to that is definitely "yes."
As much as 4e may have spurred others to look into the OSR, the creation of the OSR had already happened before 4e was announced. OSRIC was published and had more than 30 products for it before 4e's publication date.
Encounter Critical, Mazes & Minotaurs, Labyrinth Lord, Mutant Future, BFRPG, Swords & Wizardry, and Fight On! magazine all preceded 4e's release.
There were kind of two waves. First, with 3e, there was an upsurge in interest in D&D, particularly "old school" D&D. In 2000, WotC was going "back to the dungeon" and Necro was offering "3rd edition rules and 1st edition feel." Hackmaster followed in 2001, and in the first half of the decade, you saw a lot of attempts to latch on to some "old school cred" ("fishing for grognards" is what I called it): the Judges Guild products, the Blackmoor products, Goodman's DCC, and really, culminating with Troll Lord's Castles & Crusades. All were by professional game designers and all were using "updated" rules to present "old school" settings/scenarios.
At the exact same time, the Internet was becoming a much larger part of everyone's lives, and people were using it more and more for things they hadn't done before. One of those things was D&D. Simultaneously with the creation and growth of places like EnWorld and WotC's site, sites for disenfranchised D&D fans began to pop up. Dragonsfoot became the most prominent, but there were also places like the Guild of OD&D, the Vault of Pandius, and even WotC's own OOP board that were all popping up around 2002. These places became the breeding ground of the 2nd wave.
The 2nd wave was largely made up of consumers within the "disenfranchised" online D&D community who weren't satisfied with the professional attempts to produce "old school" products and who decided to do it themselves. Using the OGL to reproduce O(A)D&D had been floated as an idea on Dragonsfoot as early as 2003. When Troll Lords announced its project later that year, a lot of members of the community participated in the play testing. When C&C came out in 2004, to be diplomatic, there were some who were disappointed in the end result. This led to OSRIC and the retro-clone movement. This sort of mingled and intertwined with the more D&D friendly members of the indie-rpg movement of the first half of the decade to become the fan/hobbyist produced movement of blogs and fanzines that is the OSR.
Thus, in a lot of ways it was complete happenstance that the OSR was really hitting full stride when 4e was released.
