The definition of a classic motor vehicle is 25 years old, and a lot of what you would consider modern looking motorcycles on the road today are that age and older. The sports bike synonymous with Suzuki is the GSX-R, when the first Gixxer appeared it was way back in 1984 as a 400cc sports bike for the Japanese market.
The Gixxer decal has adorned a massive range of Suzuki motorcycles over the years and has always shouted performance, so yes, these and their stable mates from that era are now classic bikes.