With the common ship being used to transport and drop ODSTs, the Frigate can go in and out of atmosphere with no problem. In a Halo: Legends episode it shows the deploy of an ODST team well into space, not within a planet's atmosphere. On the other side, in Halo: ODST, the ODSTs were basically shot out like a shotgun towards the CCS ship hanging above Mombasa. Just above cloud cover.
TL;DR: It's up to the ship captain on how close or how far he wants to deploy his ODSTs.