In response to some posts I've seen lately saying that doomguards and infernals as guardians are questionable in utility, thus a new talent making them "permanent" would also be fairly useless:
Before Doomguard and Inferno were 10-minute DPS cooldown "guardians" that lasted 1 minute, they were on an hour-long cooldown and spawned permanent(ish) mobs that could act as pets.
Initially, both the Doomguard and Inferno were hostile to the caster, but Enslave Demon would allow a warlock to keep it as a pet for either ~10 minutes or indefinitely (depending on the resist/diminished returns mechanics of the current game patch). Some time after that, Inferno started spawning an already-enslaved Infernal pet, which could still be further controlled after the initial spell ended.
Both pets replaced your active demon, because they used the Enslave Demon mechanics. They both had a pet bar and could be controlled like any other pet. Infernals had no active abilities, just their fire damage aura.
Doomguards originally were melee pets with 4 abilities:
Rain of Fire (same mechanics as the warlock spell)
War Stomp (similar to the tauren racial)
Cripple (a super powerful single-target version of thunderclap/thunderfury's old haste debuff)
Dispel Magic (no cooldown)
So, for periods of time in the past, it was possible to have a permanent infernal or doomguard pet. They were controlled just like other pets and in the case of the doomguard had a full suite of demon abilities.
I think it's safe to assume that Demonic Servitude will, at the very least, offer the same level of control to the "new" pets and probably a set of new abilities to use as well.