I have a D5300 that I wish to use my Super Takumar 200mm f/4 on for astrophotography. However, I am of course unable to achieve infinity focus with it. If I were to use a teleconverter, would that push the focal plane back far enough to focus at infinity?
If it's the usual teleconverter (usually 1.4x or 2x) it won't change anything. You can't focus to infinity is because your registration distance is longer that the focus distance. The teleconverter changes the focal length of your lens but not its focus distance.
There are devices that look a bit like teleconverters (they go between the lens and the camera) with an additional lens that "pushes back" the focusing distance, and so let you use the M42 lenses on Nikon bodies. Plenty to find on Amazon, looking for "M42 Nikon", but most seem too cheap to feature a quality lens.