No you should be able to install to G:\ if it is not a network drive but a system drive or partition.
Instead of using the installer version with XP SP3 try the EXE (7zip) self extracting version and extract the contents to G:\ which will put all the files in G:\xampp then run the setup_xampp.bat file to set all the paths.
Then run G:\xampp\xampp-control.exe the XAMPP Control Panel and select Start Apache and Start MySQL but do not click on the Admin... buttons or you may have problems.
Then go to http://locahost
and select your language and then test all the demos including the CD collection which will verify MySQL is working.
BTW C:\ drive is the default but is not essential to use this drive.