Answer: The short and sweet answer here is NO! When you get an invitation to the shower, you can expect to get an invitation to the wedding. It is considered extremely discourteous to invite a guest to any pre-wedding event but not the wedding. It will come across like the guest is good enough to give a gift at the shower, but not important enough to be invited to the wedding. If she is keeping the wedding guest list short, keep your shower guest list just as short.
At the end of the day, you don’t want people to look back and think that their “presents” were welcome but not their “presence.”