As long as the SharePoint server is available to them (i.e. it is a public server or they are connected to a VPN that it is also attached to), then they will be able to submit to the form using the normal buttons.
EDIT: Sorry, I have assumed you are using "Rules" buttons to do submits. Add a button to the form from the top menu in InfoPath, choose a rules button and then set the rule to be submit to data connection. Select the Main Data Connection and the emailed user will be able to submit the form. They user will need InfoPath installed on their PC though.