Is it Possible to Trigger a Function when DialogChoice is selected via LocalScript?

I think yes, put a local script into startercharacterscripts. This is an example:

workspace.Dialog.Head.Dialog.DialogChoiceSelected:Connect(function(player, dialog)
	print(dialog.Name .." ".. player.Name) -- dialog.Name prints Choice1 for me, because that's the name of the choice, and player prints the player's name who clicked
	--I was just show the arguments, of course you can write your code there, or FireServer from there.
end)

Possible with Remote Events too..