If a person exercises very often would it make them less likely to have elevated liver function tests even if there was potentially damage there?

No: No. Staying active and maintaining a healthy weight is certainly good for all of your organs, liver included (reduces risk of fatty liver disease), but it would not mask or conceal significant liver damage or inflammation.

Exercise: Unlikely to have elevated liver function if you are healthy and exercising. What potential damage were you concerned about?

Yes: The most common cause for elevated liver enzymes is Non Alcoholic Fatty Liver Disease(NAFLD). Insulin resistance due to obesity is a major cause of NAFLD and exercise can reduce insulin resistance and obesity and can reduce elevated liver enzymes in early NAFLD.