can I install my wifi driver

The debian-live system comes with an overlay filesystem. That means that you can change all files, but the changes are not written to the (probably read-only) medium, but kept in ram, more precisely in a tmpfs (laid over the read only squashfs). This means that you can simply install packages using apt-get and it also means that your installed packages are gone when you reboot your system. In order to have them every time you boot, you can create your own live image (for instance using http://live-build.debian.net) and add the needed driver packages. Additional drivers (or even firmware) comes in a variety of different packages most commonly from the non-free component. Note that some drivers only come as packages ending in -dkms. Those drivers need to be compiled. I cannot tell whether this stunt works with live-build.