Productions are shot on 24fps film or 23.98fps progressive video which is then interlaced to 29.97fps. They do this to get the filmic look and feel to the production. Often DVDs are encoded at 23.98fps in order to offer a better "progressive" image and save about 20% of the space resulting in higher quality image/more space available on the disc.
Newer TVs are progressive and can actually deal with 23.98, but older ones can only show 29.97 and therefore the typical setup has the DVD player adding pulldown to the 23.98 DVD in order for it to display properly. Progressive scan players preserve the source 23.98 image and output it to a "modern" TV for the best quality possible.
Anyhow, if you are recording off of SD cable then your source is most definitely 29.97fps interlaced. You are correct that at one point the program existed at 23.98 and therefore it should be possible to remove the 3:2:3:2 pulldown extracting the 23.98 source. I have done this with source material of various sort from a DVX-100 using FCP and it went off without a hitch. I don't see why you couldn't do it with TV programming, providing the interlaced source frames can be reconstructed into progressive frames. That is, that they haven't been modified somehow in the process of broadcasting, adding titles, etc... I know its a lot to grasp...

I guess the only way to know is to try and see what happens!

If you can, try the pulldown removal in FCP, it should analyze your footage and process it if everything is good...
Look for "reverse telecine" as huntercr said.