Yes, Look at the list of actions on the properties dialog for the button. There's a submit form action. For the URL on this action use the URL format "mailto:email@example.com"
Set any field you want filled in to "Required", also on the properties dialog.
Here's an Acrobat XI tuturial on setting the field properties, there are some UI differences between this and Acrobat DC, but not much:
I've recently created a form utilizing this feature. Unfortunately, there are some users who are reporting that they have completed and submitted the form, but I am not receiving the email. However, I am receiving others without any problems. Is this limited based on how/what software the are using?
If they are using non-Adobe applications to fill in the file it's likely that it won't work at all. Ask them for specifics.
Thank you so much for your answer! Just what I wanted!
Does anyone know whether you can get this to open into Outlook for IOS rather than only the default IOS mail app?
At the moment it seems like only the IOS mail app is available.