Not only do you get catastrophic depressurisation and the tyre bead falling off the rim, but on a rear wheel in particular you can get the semi-detached strip of razor sharp rim slashing at your calf.
And if its the front then you will likely have parts or rim get caught in your front brake causing InstaEndo™
To Endo, you need grip. Since you're either already running on the rim or on a tyre which has no purchase on the rim, this seems unlikely. A front end washout isn't any more pleasant than an Endo, but it tends to break a different assortment of bones :-)
Indeed - although as I found out during a recent CX race, 0psi in the front gives quite impressive grip in deep mud....
But you are correct - on the road, its more likely to wash out than send you over the bars, although neither are scenarios I would wish to encounter...
And if its the front then you will likely have parts or rim get caught in your front brake causing InstaEndo™