Is it possible to test a Live-CD/USB by booting from it, adding drivers for a Broadcom wireless card, rebooting after that and have the drivers installed to keep on testing the Live-CD/USB?
What you're talking about doing refers to having a persistent USB Drive. With what you currently are using yes, you can reboot it but no, you won't be able to save anything to it. An option have though is to make a LiveUSB that is able to be persistent, (Able to hold changes and save them, like saving a word document etc.) then you'd most likely be able to do what you're asking. To do this I recommend you use a USB Flash drive that has a minimum of 4GB of free memory, preferably 8GB if you have it. A (hopefully anyway) simple way to do this follows.
Please Note: This tutorial is based for those with Windows Systems, and are trying out GNU/Linux on the aforementioned system.
What You Will Need
What To Do
P.S. If you need more info please do not hesitate to let me know...
This is a very similar question as this AU Question and step-by-step answer.
Ignore the "nightly download" part of the answer - just use the ISO you have downloaded to install onto a USB stick.
Once installed, you can Activate the broadcom drivers in the Additional Hardware window.