In general, warranties run from the date of purchase. In order to make a warranty claim, you have to satisfy the manufacturer that you are making the claim within the specified time period.
"Registration" is mainly a marketing tool: it lets the manufacturer know a bit more about its customers. In some cases, registering a product may be used by the manufacturer to send recall notices or other important information about the product that comes
to light.
Sometimes registering a product will result in the manufacturer's web site showing you when your warranty expires. However, in the event you were to make a claim under the warranty, the manufacturer would still require proof of purchase before honoring
the warranty. Unless the warranty registration process involves uploading a proof of purchase at the time of registration (and I can't recall ever seeing anything like that), I doubt that registering a product would satisfy the manufacturer that your claim
was timely.
Bottom line: save your receipt and perhaps a serial number from the packaging if you think you might ever have to make a warranty claim.
In your case, you should also read the "fine print" carefully to determine what warranty protection is available for purchases made outside the United States.
See
https://www.consumerreports.org/cro/2013/12/do-you-need-to-register-new-products-you-buy/index.htm
