To find out if it's ok to drive your Chevy Tahoe with the service engine soon light on we need to know what is causing the light to turn on in the first place. If it's not transmission related and you do not notice any driveability issue you might be okay with driving it for a short period of time until you have time to get the problem diagnosed and repaired.
As far as the "emission leak", the term is a bit vague. We can not say whether the auto parts store is referring to an exhaust leak, or high oxygen content in the exhaust, or perhaps a faulty oxygen sensor. You will need to have a smog check repair station (specifically) diagnose your Chevy Tahoe's service engine soon light fault.