I have never tried testing to see if die "$!" provides more information than die "$!\n".

It does:

$ perl -e 'open FOO, "<", "dontexist" or die "$!\n"'
No such file or directory
$ perl -e 'open FOO, "<", "dontexist" or die "$!"'
No such file or directory at -e line 1.
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It can also provide information on the currently open file, see e.g. second example here.

I was not able to find anything that indicated that "\n" would affect the contents of $!.

AFAIK it doesn't. Perhaps Laurent_R meant to say "You get more information from die without it."