Looks like…nope! Just ran into this same issue.
Per this post an embed does work if a) I whitelist the drive.google.com source domain AND b) I paste in the complete iframe HTML rather than the raw Google Drive URL.
However I think the main issue here is that as user wouldn’t necessarily think to grab the embed code rather than just copying and pasting the URL the same way you would a YouTube link.
(Yes I realize that Google Drive is a very different service than YouTube…but when you click play on a video in Google Drive, the video plays in what looks exactly like the YouTube player, so I think understandable that an average user might assume they’d work similarly!)
Also an issue that, as mentioned here, the video appears to display in the preview (actual thumbnail shows at least), but upon posting just shows the tiny blank non-functional preview. For example:
If it’s not possible to get these embeds to work (with onebox as opposed to iframe workaround), I’d suggest it might be worth adding an exception to just not onebox them at all.
Regardless of technical cause, this weird looks-like-an-embedded-player-but-actually-non-functional-little-box-that-isn’t-even-clickable I think is worse than just defaulting to a totally un-oneboxed link.