Lol, I'm way overthinking this… It looks like "sugoi dokuta" shows up a lot on it's own, but our boy "sugoi dokuta K" is definitely the top suggested search for sugoi docters. There's also a bunch of other "doctor K", a 1999 korean movie, and an irl person calling themselves dr K in the west.
Seems like at least the latter is unlikely to be referencing the 1988 manga, but the former may be.
There's also other examples of name shortening to K, but being specifically "スーパードクターK" feels too close to just be coincidence. The suffix "Ko" it seems, mean "child" and is used on female names to make them seem cutesy. So K-Ko is like, trying to be a cutesy version of this epic doctor, which kinda fits her.
I haven't read the manga though. It could be there are other things that make this joke make more sense, or given the amount of time Dr K had been out for when magipoka was made, it could be a direct reference, but only to the most surface knowledge of "cool doctor name".