Sort of. It's the first argument after the event, yes, but the global 'argN' variables have been gone for a while now. (I'm guessing you're looking at older code or a slightly outdated tutorial?) What you want is something like
function Frame_OnEvent(self, event, ...)
if event == "ADDON_LOADED" then
local name = ...
elseif event == "SOMETHING_WITH_MANY_ARGS" then
local arg1, arg2, arg3, arg4 = ....
do_stuff_with (arg1, arg3, arg4) -- arg2 not invited to parties anymore
elseif event == "PLAYER_LOGOUT" then
print("LOGOUT") -- won't see this anyhow because chat frames will have stopped responding
There is more than one way to write an event handler, but that's a simple one to get started with.