No, because Psych Up only copies the stat changes, and inherits nothing else. So while Blissey originally boosted with Minimize, Gardevoir is only copying the stat change, and nothing else.
Source: Looked it up and came to that conclusion.
Minimize raises Evasion by two stages. Another move that raises evasion is Double Team. However when a crushing move such as Stomp or Body Slam is used on a Pokemon with Double Team evasion the power is not doubled. The Pokemon who uses Psych Up only copies stat changes nothing else.
TL;DR: Copies stat changes and nothing else.
Another thing I think supports my answer is that Crushing moves are only doubled in power vs Pokemon who have used Minimize specifically. So the coding of the games would be unlikely to determine whether Psych Up has copied from a Pokemon who used Minimize vs a Pokemon that used Double Team.
Pages used: Double Team | Minimize | GameFAQs | Bulbapedia: Psych Up