As far as I know: yes. The firebox of the Spirit E310 has the same dimensions as the firebox of the 3 burner Genesis Silver, Gold,... I have the elevated warming rack from the Spirit 300 in my Genesis Gold.
But I think the motor needs to mounted on the right side on the Spirit. https://www.amazon.com/exec/obidos/ASIN/B00MQ7X250/tvwb-20