No, Brand Registry will not help stop this. Gray imports are genuine products intended for sale in one country, which are imported into another country that the brand owner did not want those particular products to be sold in. These unauthorized imports might be identical to the local product, or the packaging or product might vary in some way.
Gray imports, also known as parallel imports, or a distribution rather than an authenticity issue. The Brand Registry team enforces IP infringement and Amazon policy violations only, they don’t help brands control distribution.
However, if the gray market import differs in some way from the product usually sold in the country, you can do a test buy to check, then report it as “not as described”.