Yes it is. The inch is defined as 25.4 millimeters. That’s right; this is not a mere metric equivalent, but the definition of the inch (long gone are the days when it was defined as 1/36 of a the standard golden yard held in London).
Many people think that “imperial” in expressions like “imperial units” refer to the British Empire. Actually they go back to the Roman Empire, and the word should be used with caution. For example, the “imperial gallon” is 4.504 litres, but the US gallon is 20% smaller, at 3.785 gallons (*see below). It’s a long story, but it goes back to the days when beer and grain and other goods were all measured by volume but the volumes were not the same for all goods.
So we tend to refer to “US units” – the British, Australians and Canadians officially gave them up years ago – as opposed to “metric units”. But take care; the US officially went “metric” in the late 19th century, although metric units have never been obligatory. And all the obviously non-metric units such as the inch have in fact been defined in terms of SI units for decades.
So it’s not really correct to refer to “imperial” versus “metric” units. Instead we should talk about American and SI (Système International) units.
*Note: Brits often believe that American cars are less efficient than British ones, because they go fewer miles per gallon of petrol (US: gasoline). Logical enough, since the US gallon is smaller.