I just checked this AM. outside temp is 44. Inside set point 74. T-stat saying 74 and holding. Unit is on. 8 kw strip. Drawing 2.5 amps so I guess I'm good to go.
You can always just disconnect the back up wire and connect it again if you should need to. I suspect the Ecobee connects to your wifi and so gets the outdoor temp from that unless they wired in a remote sensor. I doubt that because you said you had the stat before this unit was installed.