I started using the Nokia Mail for Exchange client for Nokia S40 devices, version 0.1.34 on my Nokia 302 phone (software version 14.53). Once you turn the application on, it stays online all the time and the connection to internet is on, even when not needed. Even after changing sync schedule to 'manually' - it stays online all the time, which is not the best idea for battery capacity.
It is also impossible to simply turn the application off - you can only hide it, but it is still running in background. In my opinion there should be some possibility to switch it off.