As a F2P stand-alone PC player, this is false. I can absolutely use GunSmith to build custom weapons to set up custom classes and buy them from Loadout Drops.
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If I'm understanding correctly, OP is saying when he first lands from his chute and picks up a weapon, his pistol on the ground is called a "Custom Pistol" and it has the pink hue to it that other Custom weapons get when you loot other players you've killed. So he's asking if he sets up a custom class with that same starting pistol but modified w/attachements, if he will drop from the plane with that same modified pistol w/attachements.
And OP my best guess is no.
Everyone drops from the plane with the same "loadout" - that makes it fair. You have to buy a Loadout to get your custom weapons.