With media mail it shouldn't make a difference. But with 1st class it might. Most likely not though.  You could ask your local post office. 

My house is in one town but serviced by another town's post office.  Which is really stupid because the post office for the town I actually live in is right near my houe whereas the one the delivers my mail is all the way across town.  I don't know why they did it this way.  Apparently I'm right on the town line.  It was really confusing when we bought our house because the contracts, appaisal, listing, survey etc.., say one town but for mail we have to use the other.  Anyway: I brought a bunch of books to mail to the closer PO and asked if it would be a problem-I was told that it was perfectly find to mail them from there.  Another time I mailed books from a dif post office in a 3rd town and again no problem.

So I would say you are probably ok.  The next time you have one that shows as first class-you might want to use the post offices website to just double check that the postage is the same from your work zip code.  Just to see.

it doesnt really matter

I live in one zip code and since i work at Fedex office ((formerly fedex Kinkos (formerly Kinkos)

I would print out PBS labels at work and mail from that zip code never had a problem and the mail man pick up them with the rest of the outgoing mail

Thanks for the info!  I'll stick them in the mailbox by work :)

If I am remembering correctly from a USPS employee's answer long ago, the mailed from zip code "credits" the post office with said zip code for the piece of mail. 

So if you want to make sure your bluebox near work stays there, change the zip code to that one.