In a word,
NO.
If done well, stropping is likely the best way to maintain a good working edge on a blade (if not excellent), and minimize unnecessary metal removal at the same time.
Stropping with poor technique (poor angle control, too-heavy pressure), or using too-aggressive compound unnecessarily, will do more harm than good. But, if one's technique is sound, and the compound or stropping substrate is well-selected for the needs of the edge, one can strop virtually all day without harming an edge. There will likely be some point at which the noticeable improvement in sharpness will slow or cease, however.
BTW, two of my favorite and BEST strops are old belts (sueded sides), used with green compound and also bare. One belt is relatively new, the other is one that my father wore while serving in the Army about 60 years ago. That leather is some wonderful stuff. Leather does not have to be new or pristine (or expensive, most importantly) to work excellently on an edge. Keeping it clean, within reason, is always good, but there's no significant advantage in getting 'obsessive' (this, coming from ME

) about the cleanliness of it. Wipe it down between sharpening sessions, and also wipe down your blade after it's been on the stones or after using coarser grit compounds.
Stropping by hand won't heat a blade enough to damage it. Doing so on a powered leather wheel, as with any powered sharpener, very well might damage it, in inexperienced or careless hands.
David