All servers flooded by salt water, is it possible to recover data from multi-platter drives?

I almost cringe to do this, but if you're serious about recovering your data, and you don't have backups, you'll need a higher-end data recovery service.
Watch out for fly-by-nights shops that will be peddling/scamming in your area, and go with an actual top-tier data recovery service. (And be prepared to pay $$$$ for it.)

Here's a list of what to look at:

1. Your data.

   • These services are expensive, generally starting at over $1000 a drive, so you need to decide if your data's really worth the cost of recovering it.
     
     

2. Recovery company's history.

   • If they haven't been around for at least several years, and in the data recovery field, they're probably not worth considering.
   • Top-tier companies will have a portfolio of the more interesting or challenging recoveries they've done. Take a look at those, and make sure the guys you choose have enough experience with water-damaged hard drives that it's just another day in the office for them.
     
     

3. Recovery company's clientele

   • Top tier companies are generally contracted by law enforcement and law firms for cases where someone deliberately tried to destroy a hard drive, so if you find one that's worked with a lot of police departments or on a lot of legal cases, they're probably a good one. (Generally this becomes public record at trial too, allowing them to disclose their involvement.)
     
     

4. Recovery company's facilities

   • Not that you should expect a tour, but you're looking for clean rooms, labs and proprietary or custom tools they've developed to recover data from physically damaged media.

And I don't generally do this, but since the other answer has a link I'd be a little wary of, I'll throw out a recommendation of sorts. These guys are good, (expensive as hell, but good), and if you decide to go down this route you should look at them, if only for nothing more than to compare other data recovery services against.

EDIT: And as mentioned in the comments by @Grant, DO NOT take it to a lower-quality data recovery service first, because both the data recovery process itself and the passage of time will do [additional] irreversible damage to your drives. If you decide later to try someone better or more qualified, your earlier decision will have increased the cost and decreased the results.

There are already many companies providing services for this, for example 24HourData (their site has a list of drives they support).

While you figure out your next steps keep these things in mind
(from Top Tips for Liquid Damaged Data Storage Devices)

1. Do not try to power on a flood damaged hard drive
   bad things happen to good hard drives when this is done!

2. Strange as it may seem, in most cases it is not wise to allow your device to dry off.
   Sealing your water damaged media in an air tight container and getting it to a data recovery company is definitely the best option if you need your data back.

3. Do not presume that only the electronics will be affected and attempt to swap PCBs or components - doing so may prove dangerous to yourself and your drive.

4. Don't open up your hard drive under any circumstances
   (unless of course you don't mind losing you data).

5. If you have a backup copy of your data and therefore don't need a data recovery service, backup the backup, they say that bad luck comes in threes!

_{Highlights in these points are mine.}

I know @HopelessN00b already mentioned this, and I'm not affiliated with them, but try this: Kroll Ontrack

From what I can tell, they handle some of the most difficult data recovery cases, including server, RAID, and forensic data recovery. Given that this is one of the leading data recovery companies, expect to pay dearly for their services. More information on their server data recovery services can be found here.

A cheap data recovery service is not the way to go. Data recovery is inherently a expensive and labor-intensive service, requiring state-of-the-art cleanrooms, highly specialized tools, and extensive experience. Even Ontrack itself says:

Note: Trying this on your own or through an inexperienced data recovery provider may lead to further damage to the drive.

To answer your question, yes, it should be able to recover data and store it into a working drive(s). This is what Kroll Ontrack does.

Is it possible for each platter in a multi-platter drive to be separated, cleaned, imaged, and merged into a new virtual drive for data recovery?

As you would have read in other articles, the answer to this question is "yes". What you would not have read yet is that it is not an unconditional "yes". Data recovery companies would do what is called a "best-effort recovery" - i.e. they will clean the platters and use specialized equipment to read your data off them, but there is absolutely no guarantee your data is still what it used to be - be prepared for losses. Also, be prepared for a massive bill, even if your data could only be partially recovered.

Hard disk drives are not hermetically sealed, they have a venting hole so pressure differences between inside and outside would not deform the drive's case. So salt water would be able intrude into the drive upon immersion. And as is widely known, salt water is going to cause massive corrosion. The magnetic material on the platters is typically protected by carbon overcoat, but it would be overly optimistic to believe that no data bits would be affected.