If I gave USPS the right address but the wrong zip code will they still ship it to me?

Perhaps, and most likely yes. However, it may take a bit longer. If your address also exists in the zip code that you provided (unlikely, and rare), it may be delivered to where it was addressed.

However, it is more likely that the item will be rerouted to your actual location, once the correct zipcode is determined by the company, at the original zipcode destination's USPS sorting office. You may get lucky and they may determine the correct zipcode early enough to reroute it efficiently.

First, they sort by state, then by zip. If the zip is not for your state, they may detect it and computers will determine the correct zip based on the state and street address. In the event that there are multiple street address matches within the state and the zip is not closer to either, they may elect to return the package to the sender, rather than deliver to the incorrect address.