They're very likely to be causing myocarditis through the same mechanism involving the spike protein, which means your scenario is unlikely. Myocarditis prevalence among college athletes who have recovered from a COVID-19 infection (even asymptomatic) is so high that some conferences require comprehensive cardiac testing before they can return to play. https://www.thecardiologyadvisor.com/general-cardiology/hear...

Exercising while infected is known to increase risk. If you get the vaccine, you will be told not to exert yourself for some time after. If you get infected, you might have no idea that you should stop exercising unless and until you're symptomatic. https://www.bvhealthsystem.org/expert-health-articles/covid-...