When I first tried MailDroid a few years back I really liked it but it definitely did drain off my battery. HOWEVER the current version has no noticeable impact on battery life - I have not seen any change in battery life since installing it, and GSam Battery Monitor (which tells me which apps are sucking battery) does not list MailDroid as one of them.
The developer has done a great job not only on look and feel and feature but also on performance.