Short answer: if it’s a newer Nikon camera model (last year or two), probably no. Keep reading and I’ll give you a way to come up with a more definitive answer.
First, let’s define gray market. Gray market is product that Nikon dumps directly from the factory to large distributors and resellers—mostly into SE Asia—basically without warranty or support.
Normally a Nikon camera is sold from Nikon corporate to a Nikon subsidiary, where it is then resold to authorized dealers in that country/region. Nikon uses serial numbers to keep track of this, and these so-called “official imports” almost always come with a printed warranty certificate with that serial number on it.
Here’s the thing: under virtually no circumstances will NikonUSA service a camera they didn’t directly import, in other words, a gray market camera. They won’t provide warranty service, nor will they even repair the camera for money. The one exception appears to be cameras for which there is a worldwide service advisory active (e.g. the D600, D800, or D750 models).
Outside the US what a Nikon subsidiary will or won’t repair is controlled by local law. In some areas (e.g. parts of the EU) you can get gray market product repaired by Nikon because of specific local laws, in others you can’t.
NikonUSA (and some other subsidiaries) authorizes some third-party repair shops to work on Nikon gear, and sells them test equipment, training, and parts. And that’s where we get to the short answer, above: for new cameras, that gear, training, and parts isn’t made available in a timely fashion.
For example, as I update this article in Spring 2017, the following Nikon bodies currently aren’t repairable by the independent authorized repair centers because they don’t have the gear, training, or parts to do so: D5600, D7200, D7500, D610, D750, D500, D4/D4s, and D5. In fact, it was only recently that the D5500, D7100, D800, and D810 models were added to being serviced by independent authorized repair shops.
Here’s how you find out if someone will repair your gray market camera: go to this NikonUSA Web page and enter your model number. If authorized repair stations other than the two NikonUSA ones appear (see arrow in the example, below), then it’s likely that you can get repairs of your gray market product.
So yes, older gray market cameras can often be repaired by one of the authorized repair shops here in the US, but the newest ones often can’t be. So by buying gray market you’re taking the risk of ending up with an inoperable camera that can’t be repaired for some time.
This is just “repair,” as in repairs that you pay for. What about warranty work? Nope. You get no factory warranty repairs done this way (again, unless Nikon has made an exception via a worldwide service advisory).
But what about the “warranty” that most gray market camera sellers advertise you as getting? Based upon reporting from this site’s readership, I’d say that this is a hit or miss proposition. Some of the more reliable sources of gray market will do swap outs of product in lieu of actual repair. A few repair if they can. But I’ve heard plenty of horror stories where a gray market seller didn’t honor the warranty they advertised (or worse, the actual warranty provider was now “out of business”).
My advice is this: if you’re buying a “current” Nikon body your best bet is to avoid gray market product. If you’re buying an older Nikon body that you know is repairable by the independent authorized repair stations, then perhaps the lower price of the gray market product would be tempting.