If I update my iPhone to ios 7 will I be asked to choose a carrier?

My iPhone has no service and I would like to update it to ios 7. But I'm afraid that I would need service on my phone to unlock it once its on.

No. But it may give you the error saying it has no SIM.

It's no longer an iPhone--it's now an iPod=no service. Updating will just upgrade the firmware--the stuff that makes it run in the first place. Updates do not require service.
Best luck.

More than likely after the update it would take you to the activation process. May be able to skip past it though I doubt it. If you can't it you would at least have to use a SIM to get through that part.