No, pretty sure not. First of all, the “buy” date is the date it vests, not the date it was initially granted. Secondly, you pay normal income tax on stock grants. So if $100 of stock vests today, you pay normal income tax on $100, and the cost basis and “buy” date are set to $100 and today. If you hang one to the stock for a year, then sure, you get long term gains, but then it’s the same boat as if you just got cash then bought it for $100.

ESPP can be a bit different, because you get a discount on the stock, but that discount is also taxed at normal income rates, and anyways is capped at like 15% or something.