If a game crashes, should it create an "acklog.txt" file?

If so, what does it mean if no file is created?

It probably means you did not start the engine with proper debug flags.

OK, this is a published version of the game. Is there a way for a published game to produce an Acklog file?

You need to add -diag in the wdl/starter file iirc (search for wdl in the manual for more info and an example).
You can also try setting diag_mode in your script but I think that is more for during the game and not on startup.

Example from my own game / wdl file;

WINDOW WINSTART
{
MODE STANDARD;
COMMAND "-diag";
}

Also if you use the default starting up screen it also shows the errors (but that ofcourse means not having a fancy custom startup screen).