K, the Lanvill Stability Factor has to be greater than 1 to be stable, when you come to analyse the stability, scattering factors and reflection in LNA.
When K is greater than 1 and ΔS is less than one, the device is unconditionally stable for any combination of source and load impedances. If, on the other hand, K calculates to be less than 1 or ΔS to be greater than 1, the device is potentially unstable and is likely to oscillate for certain combinations of source and load impedance. With K less than 1, or ΔS greater than 1, you must be extremely careful in choosing the source and load impedances. Those conditions do not mean that the device cannot be used, but merely that it will be more difficult to use.
Gummel-Poon is strictly a BJT transistor model targeted on HFE (DC gain) and nothing to do with K and LNA design.