I'm curious, cause I already have an Escavalier but want an Accelgor to trade to my sister.
Plus its an interesting question.
No it wouldn't.
"It evolves into Accelgor when traded for a Karrablast, which evolves into Escavalier simultaneously. Neither evolves if at least one holds an Everstone during the trade."
Source: http://bulbapedia.bulbagarden.net/wiki/Shelmet_(Pokémon)
Hope I helped :)
The everstone prevents evolution, so no.
Source: Experience
Yep it stop a Pokemon from evolution