Not sure on a 04 Boxster but on the Coxster the only issue which comes up is the PSM error. The book says to simply to turn the wheel several times, but I've found it will only clear once you start driving, so go easy to start with.
If you do not leave the battery off for hours or days then there should be no problem at all, and only the PSM warning so come up and clear afterwards.
I got it to work. I found some instructions that pointed out that radio codes apply only to 94 through '02 Boxsters. Swapped the battery out and all is well.
The part I wasn't sure about was the positive connection to the battery through the fuse box. I wasn't sure how to do that until I found some instructions that explained how the positive connection is made through the red "button" with the open hood marked on it. You pull it out to provide a connection to the battery and ground the negative to the door latch.
So, no code problems and I've got my new battery in.