Supertele autofocus starts to squeal

Whatever is causing the noise is causing excessive wear to the parts that are making the noise.

Get it serviced as soon as possible or risk prematurely having to replace parts instead of only having to have them lubricated.

As the mechanic in a 1970s commercial for Fram oil filters says:

"This is a main bearing job, about $200. And this, this is a Fram oil filter. It's about $4. If the guy who owns this car had put four bucks into one of these (holds up $4 Fram oil filter) when he had his oil changed, chances are he wouldn't be putting two hundred bucks into one of these (holds up a ruined rod bearing). Well, the choice is yours. You can (holds up $4 Fram oil filter) pay me now... or (looks at ruined bearing and shrugs) ... pay me later."

If you have the older version that was replaced in 2013 with the newer one, replacement parts may no longer be available. Even if they are, since Nikon no longer sells parts to anyone, you'll have to pay Nikon to fix the lens. You can often find third-party repair services that can do a clean-and-lubricate much cheaper than what Nikon will charge.

What you are describing is most likely the AF motor itself. Nikon uses two types of focus motors in their AF-S lenses. One is an ultrasonic ring type and one is gear drive. IME a squeaking ultrasonic motor is typically less of an imminent failure issue than if it is the gear drive type. You can tell which type it has by counting the number of electrical contacts on the lens. Gear drive has 8 contacts; ring type has 10 contacts... I think the 200-400 has the ring type USM.

If it is the motor a CLA service is not likely to fix the issue; and the repair that Nikon will almost certainly insist on is replacing the focus motor. I would consider just using the lens until the motor dies; and it may not. I had a 300/4 develop a squeak, had the motor replaced under warranty, squeak returned out of warranty, and it was still operational like that many years later when I sold it. However, if AF failure would be critical for you then you should get it repaired now (or if it's just really annoying like my 400/2.8 has recently become).

AFAIK, Nikon does not clean/lubricate the motor when there is an issue; it's always replacement. And if you do not agree to all of the service/repairs Nikon says are needed then they won't service it at all. Cost is likely to be in the $500 range.