Pawns take their primary weapon with them on caravans visible next to them in the organizing screen; it's not even an option to bring your primary with you or not.
However when organizing a caravan the sidearm *might* be already selected, but so are weapons already loaded onto animals or in pawn's inventory with no distinction. What's worse, is after changing pawn's assignment into or out of a caravan (even for the first time!) their sidearms remain in the caravan inventory and I have to remember which colonist is holding on to which sidearms and where they're going because when I make a mistake their trusty melee weapon is off to get sold in bulk with the rest of my loot, or left at home (dropped in the field) when we go raiding.