The real problem with your model is not the power vacuums, violation of succession wishes, or any of the other issues that are going to be raised here. The real problem is the assumption that no-one can contest a selection of a new emperor.
Of course they can; it happens all the time, even now in destabilised countries. Every attempt at revolution, every act of terrorism, every protest on the streets is in fact an example of people doing exactly that; contesting the status quo.
There is an old saying; "The only power others have over you is that which you give them." This has been demonstrated with every regime change there has ever been, insofar as the law only works in a society if everyone implicitly agrees to be bound to it. Sure, there are criminals out there who change their ways after a stint in prison, and even those who don't, and they're managed by force.
But what if those 'criminals' have bigger guns than the police do?
Ultimately, regardless of whether or not the emperor appoints this council and whether or not they get final say in the succession will come down to their ability to back it up with either popular support and/or force. So, let's really look at this model in terms of what people have to lose if they don't follow the status quo.
The council appointees are given their power (like a privy council with teeth) by the emperor, so they have a vested interest in backing him or her while (s)he's alive. They know that which is why they don't buck the system. But, the people on this council are highly unlikely to be mere lackeys; they're going to know who's popular among the people, who's not and how the military leaders feel about it all. Add to that the fact that their membership on the council makes them influential and (ideally) rich, and when the emperor dies they themselves have a vested interest in the continuance of the state with minimal disruption during the transition of power.
So; the emperor 'prefers' a candidate that's popular with the people and the military, it's a no brainer, especially if that candidate also still likes the privy council.
If your emperor picks a candidate that is unpopular with both the people and the military, finding another candidate, one that will be grateful to the privy council for their support, is also a no-brainer. No-one's going to argue and the country just moves on after a couple of sporadic protests about regime change.
It's the boundary conditions you really have to worry about. Preferred candidates that hate the privy council, but are in tight with the military, even if unpopular with the people. That kind of thing.
Make no mistake; the privy council in your scenario will act in their own interests, but their position and title do make their interests align reasonably well with those of the state. So much so that in many cases it will be hard to see the difference between self interest and altruism. But, at the end of the day, civil war is never in anyone's interest and power is often given in social conformance so as to avoid the use of force in a manner that introduces risk to one's long term health every bit as much as one's short term health.
This is in fact the very moral that was taught to Damocles in the legend about the sword. Great power is not a means to itself as it carries with it the responsibility of the state, and one's decisions must always reflect the welfare of those who grant that power to you by NOT rising in rebellion.
As such, while examples like the Cardinal's Conclave for electing new popes, there are plenty of examples through history where succession has either been declared or ratified by some form of noble council. But, there are also as many examples of where someone with enough numbers and swords decided his choice was better and did something about it.
Whether in a democracy, authoritarian dictatorship or empire, it's a wise ruler (and ruling council) that always takes the views of the people and the protectors of the people into account, and your council will do exactly that if the empire is to continue.