Hi Katy, welcome to the InfoPath Dev Forums.
Yes what you want to do is totally possible with InfoPath.
Just design your data view first, then when you are all done you design the email view (you could copy the entire "date view" over to the email view to speed things up). For the email view you probably want to use expression boxes for the fields rather than a text field, dropdown, multi select etc.
In your rules to submit the form via email add a rule to switch to the email view before the email fires.
Hope that makes sense
Ted