Once you log into your SE account from your PS3, your early access code will be linked to your account at that time.
We'll find out on the 24th, but while I linked it on the PS3 ( and installed the update that popped up for me today ) it's still distinctly a PS3 only early access on my end.
EDIT: Nope, looks like I'm stuck playing on PS3 this weekend according to this
and a lot of other people under the same situation. Annoying, but it's only a few days.
My initial statement was just in regards to why Early Access wasn't showing up on the SE account even though it's installed on PS3. The simple fact of the matter is, you haven't been able to log into your SE account from the PS3 to make the association yet. I wasn't commenting on whether this gives you early PC access as well.
However, regarding the support desk chat, I would take that information with a grain of salt. They don't have all the answers for every possible scenario, and this case is potentially off-script. In that case they would resort to telling you the least disappointing outcome (i.e. PS3 only access) rather than make a false promise (i.e. saying you can access from PC only to discover you can't).
You do have to link your PSN account to an SE account, and doing so could possibly grant you early access on PC if it's the same account you use for PC. It comes down to whether they separated Early Access permission by platform or not. We won't know for sure until they make an official statement either way, or we test it out on the 24th.