I can't speak for the sidesho but a 510 attys will go onto an (old style?) 902 battery connector (not sure if the connector is different with the new batteries) because the threading is the same and the flat bottom will make contact. You have to leave it a little loose though to get airflow. An old 902 atty won't work on a 510 connector because of the lip on the bottom of the atomizer keeps the center from making contact. The new style 902 atty with the flat connector should work on a 510 connector.
Charging is another story completely. They are both 3.7V Li-ion (4.2V for charging) batteries but I'm not sure whether the logic circuits are compatible between the 510 charger and the 902 battery circuit boards.