Discovered this in Realms; reproduced in Single Player too.

In realms, type:

"/gamemode 1"
"/summon EnderDragon"
"/gamemode 0"

The EnderDragon will spawn, but there will be no health bar. It is invincible and fixed in location. It is fully animated with sound effects, but stationary. The player in gamemode=0 can walk through the dragon without injury.

In Single Player, I created a superflat, cheats enabled and summoned one in exactly the same way with identical outcomes.

It appears to be impossible to destroy the dragon. I had to recover from backup to restore the realm to a level of sanity.