Nothing in the user manual to suggest that it will. In the earlier versions there was specific mention go ANT+ connectivity.
Nope, it won't.
There was an old comment by a Garmin rep indicating they had to make compromises with the VF4 due to available memory.
Instead of ANT+ HR sensor compatibility, they retained synchronization via ANT+ dongle, and added "Toe-to-Toe Challenge" via ANT+ with other Vivofit 4 users:
Garmin has more data on who was using HR straps with their Vivofit 1/2/3 so maybe they didn't see it as a popular feature. I would like to have seen it kept, and added back to whatever comes next - I keep a Vivofit around as a backup device in case my Forerunner ever needs warranty work.