I don't think such a check is strictly necessary to be honest with you. If the DM feels your party looks intimidating, they'll simply have the NPCs respond accordingly.
The whole point of passive checks is that it allows characters (and NPCs!) to bounce off a large amount of DCs and contested checks in the surrounding area without having to constantly ask the players to roll a d20. Passive perception works well because lots of threats (stealthed enemies, traps, pickpockets in a busy street) have DCs that your perception is checking against automatically (hence the passive part) and it works VERY well for perception.
It doesn't work so well for Intimidation though...
Intimidation is different, because, unless as a DM you are having each and every NPC in, say, a busy marketplace make DCs or saves to determine if they're intimidated or not (which would be silly and unnecessary!), you may as well just narrate if they are intimidated or not without bothering with checks at all.
Another thing I don't like about this idea is that it takes control away from the players. If a player wants to be intimidating that's their prerogative. By using a passive intimidation you're basically making it so that they're ALWAYS being intimidating, even if they actually want to try not to be.