No, emailing a document does not make any changes to a document or it's rights.
It's possible to do something like that using a Business Process. You'd need to make a standalone field called something like "recipient" (it could even be a multi-value field) that would accept the user name(s) of the person you wanted to grant access. You'd then need to add that field and fill it out. Then you could have a Business Process that would look for that field and change the access rights before mailing the person(s) a shortcut and finally removing the "recipient" field.