Yes, they do. Well, there's a 95% chance that they do (nothing is certain in the Dominations universe). However, a few related notes:
* Your example references "heavy cavalry" ... I highly recommend not investing museum resources into heavy cavalry as they are a dead troop; don't use them (instead, Heavy Tanks are awesome)
* A related question is 'do war museum stats apply to donated defensive troops?' ... the likely answer is yes but this is not yet certain
* Main hall museum statistics do show up in troop screen shot information; whereas war hall museum statistics do not
Bottom line: assume they do, but don't alter your museum upgrade decisions for this reason.