Welcome to the Forum Holmes
Lots of choices for your brother.
#1 Weld inspectors generally are not required to be welders... If you are referring to an AWS CWI the answer is a definate no, welder cert is not required to become a CWI.
Paying your own money to get certified in order to leverage your boss to pay more is a bad idea. That boss is a tight wad and a piece of paper is not going to make a difference. Good employers take it upon themselves to have their crews certified if it is necessary, and they pay them a solid wage to keep them. Thats just how it works.
A good multi process welder can make as much as an inspector, sometimes more. Most high paid inspectors have decades of experience and education/training behind them before they start making big money.
Your brother would be wise to get in touch with his local AWS section. They will be able to give him advice and support in his quest for a weld inspector position.