Not so much, no.
The "me too" is a very colloquial way of saying "I feel the same way," and it only works in some circumstances. The first person needs to make an "I" statement.
I love you.
I enjoyed my meal very much.
I enjoyed working with you.
If someone said "I am so pleased to meet you" then "me too" is too informal a response. But you could say "Likewise!" to mean that you were pleased to have met him/her.