NOTE: This is not the place to question the fundamental veracity of nuclear propulsion in aircraft and spacecraft.
For context, in a spaceplane, the higher speeds you can attain under air-breathing power the better, as they are inherently more efficient than rocket engines. In both air-breathing and rocket propulsion, using a nuclear heat source promises much higher efficiency than a chemical one, with almost infinite and ~1200 seconds specific impulse potentially being attainable, respectively. However, for any turbojet engine, principal limits in speed are the compressor inlet temperature and the maximum temperature of the hot section. In chemical jet engines, the energy density of the fuel puts a hard cap on the latter. Even notional nuclear turbojets, though, also have those same limitations due to the material constraints of constructing them.
So, in order to increase the speed of a turbojet, the compressor must be actively cooled and the temperature of the hot section boosted beyond what is normally possible. These problems could be potentially solved by using an air-breathing analogue of a LANTR (Liquid oxygen-Augmented Nuclear Thermal Rocket) cycle with elements of SABRE. First, the liquid hydrogen later used in rocket propulsion would be pumped through the compressor section, lowering its temperature while also recovering its heat energy. This would also aid in nuclear reactor thermal efficiency. Second, this hot hydrogen gas would be pumped through the nozzle, cooling it down while recovering more heat. This would then be injected at the nozzle throat. The very hot hydrogen and extremely hot nuclear-preheated air would combust at astronomical temperatures, potentially allowing higher speeds to be reached before the spaceplane would have to switch to pure rocket mode.
So, the question can be expanded and rephrased as this: Would such a "LHANTTJ" (Liquid Hydrogen-Augmented Nuclear Thermal TurboJet) engine actually produce a higher specific impulse than the subsequent pure-rocket stage and a higher exhaust velocity than reachable through the previous pure-nuclear turbojet stage? Also, would the systems be worth the extra weight?
Edit: If the answer to the first element of the above question is "yes", by about how much would the exhaust velocity and specific impulse be greater?