claimed that exercise is detrimental because it depletes the body’s finite energy?

The belief has been long documented, and Trump’s reiterated his belief on the 2016 campaign trail:

All my friends who work out all the time, they’re going for knee replacements, hip replacements — they’re a disaster. That’s exercise.

As far as modern medical science has been able to determine, this is untrue.

The New York Times – Donald Trump is Not Going Anywhere
The Washington Post – Trump thinks that exercising too much uses up the body’s finite energy

Business Insider – Trump believes some amazingly false things about exercise
The New Yorker – How Trump Could Get Fired