Health regen would be a lot harder to test, but I’d guess that it probably doesn’t. Regen doesn’t count as healing given in the score board.
It should be easy to test self-heals though, or at least it would if most of the characters that can do so didn’t have natural health regen. I’m almost 100% certain that, for example, healing received helps boost the healing Ambra gets from her own sunspots, but things like Miko’s Biosynthesis are more difficult to test since Miko naturally regenerates, so the numbers are harder to track.
For the curious, my test on lifesteal was done as an Attikus in private story, punching turrets and seeing if there is a difference from the Brawler’s Boon lifesteal when you get a 12% heal received boost item. It still only healed 12-13 per punch regardless, and I ought to have seen a bump of at least one point on the average if you do the math. Since the numbers we’re dealing with are so small, though, there’s always some room for error.
Edit: I don’t have time right this second to do more tests, but I can do so later tonight. Gives me an excuse to run through Renegade over and over for legendaries.