I have found that there are two ways to get into the HR lounge, one way is to give Glottis the ID card and another way is to use it yourself.

Now I was wondering, does choosing one of the options as opposed to the other change the puzzles in any way? Like does Glottis visit the club if you don't give him the card at all? Thanks.

Nah, You need Glottis to visit the club in order to get Chowchilla Charlies briefase. He'll inadvertently assists you.

The problem is that Glottis won't help you while he's gambling.:)