Somewhat, and their newer types (like the Ka-52) don’t have to do that. The older designs like the Mi-6, Mi-8 and the Mi-24 do because their ‘winglets’ actually generate significant lift that they sometimes need to get off the ground at full load.
On the other hand, full load for an Mi-24 is actually heavier than the CH-46E. The Mi-24 has two 2200shp Isotov turbines and its max takeoff weight is 11,500kg/25,353lbs to the twin 1250shp GE turbines and 11,022kg/24,300lbs for the CH-46E. The Mi-8 the Mi-24 is built off of can lift even more and is the most produced helicopter in world history.
Something else to note - Mi-24s have been known to shrug off Stinger and Redeye hits. A Stinger or Redeye can take them down, but it’s not a all-but-guaranteed kill like it is on a Western chopper.
I flew E’s, they had -16 engines and advertised power rating of 1870 aside.