remote is normally dead once in the ignition barrel. If evo cannot monitor the remote commands, no.
What you might be able to do though, is add a push button switch to the yellow/black (-) trigger input of the unit.
So before turning the car off, you would tap that button once and it would trigger the remote starter.
Normally, takeover is not supported on TipKeys though after activating idle mode due to fact anyone could climb in, stick their finger in the key port and turn the barrel. Remote starter will shut down on either door open or brake press if it was activating via idle mode.