I don't think so. Having ridden with both power and HR data for years I have seen how unreliable HR is as a measure of the amount of work you're doing. There are too many things that can make HR be high or low that aren't related to training stress. Say I am riding up a long climb in 105 degree heat and am overheated. My HR is right at threshold but my power is 2/3 what I can normally do. Am I getting more or less of a training benefit? Assume I am already heat acclimated, and yes I did run into this situation a couple years ago. It was interesting how obvious it was when I finally overheated.

Even for training stress it's questionable. For example I'll do three times up Mt Diablo (3200 to 3600' depending on the route) and the HR will be the same or go up for each repeat but the power will go down. Obviously I am experiencing "drift" or cumulative fatigue.