Nah. If someone can't handle a few g's in takeoff, maybe they shouldn't be flying, and should should stay home, or maybe in a nursing home. I know it sounds mean, but seriously, think about it: aircraft transport isn't always comfortable. Turbulence happens, and it can be extremely rough at times, even injuring people severely if they're not belted in. If someone is too frail to handle being launched by an aircraft carrier catapult (which, remember, also launch those big AWACS planes, not just small fighter jets), then they're not suited for handling turbulence either.

Also, don't forget, the latest generation of catapult technology is actually pretty gentle. The USS Ford's "EMALS" catapults are electromagnetic, rather than steam, and one of the big stated benefits of this is that it's gentler on the airframes than the old steam catapults. It's still going to subject the pilots/passengers to several g's, but probably lower peak acceleration than the older technology did.