Yes you can, with CS3 being as far back as they allow upgrades for. I was poking around the Adobe.com Photoshop purchase page to see if I could find out if upgrading a student edition was allowed or not and a chat window popped up and the person on the other side said the educational version was ok to upgrade from:
Please hold as we route your chat to an Adobe Representative.
Welcome to Adobe.com! My name is Vincy. May I assist you with your selection today?
Vincy: Hi, How are you doing today?
Steve: Can PS-CS3 Student Edition purchased some years ago be upgraded to PS-CS6 for the $199 price or some other price?
Steve: The PS-CS6 would not be a student edition.
Vincy: I will be happy to provide you the information.
Vincy: Yes, you can upgrade Photoshop CS3 to CS6 although it was a student version.
Steve: Ok, thank you. This was a question on the Adobe Forums just now and someone answered that a student edition could not be upgraded. Does the Adobe website have this information somewhere that I could provide a link to, or should I just copy/paste our session, here?
Vincy: I'll provide you the information.
Vincy: That's correct Student version software can't be upgraded only under education store, however it can be upgraded under retail store.
Steve: The upgrade-from choices in the retail store don't say whether the CS3 is student edition or not, and it would be bad for someone to order the upgrade and then try to install it and it not accept the serial number for the student edition. I would like to see a place on the adobe.com site that says what you're telling me. Do you have a link to such information or not?
Vincy: That's okay. It will just ask which version you have. It doesn't matter it's education version or retail version. Only the serial key matters for the upgrade.
Steve: Right, and so the question is, will a student-edition serial number be accepted as the previous-version serial-number during the install process?
Vincy: Yes, it will.
Well, good for the OP!
I may have misunderstood this previously:
»Education pricing isn't offered for upgrades. However, you can upgrade educational products at the regular upgrade prices.«
If you hang around the site long enough and it is during the hours they staff it, then it’ll pop up. I think the support chat may not be available on the weekends, but the sales area they are staffing more hours in hopes of making more sales, at least during the initial period after the new version is available. I was on the Photoshop purchase page that has the Upgrade-From and DVD or Download questions.
One thing to keep in mind was that I asked specifically about the Photoshop CS3-SE to Photoshop CS6 non-SE, and they said that was available. I would expect the other two components you mentioned also have the same upgradability, but I doubt you can upgrade from the three pieces you had to a full-blown CS6-suite of all products so if that’s what you were planning, be sure to ask someone.