That might well be what the ROKN CNO believes, but I tend to suspect it would take quite a bit longer as well as requiring more outside help.
One needs to remember that S. Korea first built a sub in the early 90's, and the KSS-III which has subs under construction is the first domestic S. Korean conventional sub design. As we have seen with Spain's S-80 design, it is easy to screw up a design even for experienced yards.
When one then factors in the need to design an adequate SSN reactor and then fit that into a sub design... Unless S. Korea has been quietly working on a SSN reactor & design for years, then there is most likely years of work before a domestic S. Korean SSN would launch.
Now the US and UK naval construction might not be the fastest, both nations have decades of experience designing and building SSN's, including the reactors. If one looks at when development work began on RN or USN SSN's, it normally takes several years to a decade between design work being initiated and the start of construction. I would expect that S. Korea will also require similar times or even greater due to a lack of prior experience with fitting and integrating a reactor.