Will the Android M developer preview get an OTA update to the stable release version? If I install the Dev Preview 3 on my Nexus 5 right now, will I get an OTA to the stable build or will I have to flash it as well?
No, you need to flash it since Google only provides the stable release as downloadable image on Factory Images for Nexus Devices.

From Official Android Developer site,


  Note: Developer Preview 3 includes final APIs and near-final system images available by both download and OTA. At the full public release of Android M later in Q3, final system images will be available by download only, so you'll need to flash manually to your test devices.