Hydrazine is used a monopropellant in Satellite OMS rockets. But interestingly enough, it's highly exothermic decomposition into ammonia, nitrogen, and hydrogen provides heat for an endothermic reaction with additional hydrazine to form hydrogen gas. So a scramjet using hydrazine would have to reactions inside it's combustion chamber: The decomposition of hydrazine and the combustion of the resulting hydrogen gas with air. And unlike hydrogen gas, hydrazine has much higher propellant density. Has this ever been considered by aerospace engineers and even tested?
Technically yes, you could use hydrazine in a scramjet.
But there's no reason to do so. The singular purpose of building a scramjet is to get air into the combustion chamber, so that you don't have to use a monopropellant, which all have high cost and poor energy density.
Kerosene or H2 won't burn without air, so you need a scramjet or an oxygen tank to burn them. Hydrazine doesn't, so you can burn it in a rocket, at higher pressure with more efficiency and better aerodynamics.
Advantage: Rocket engines have a thrust:weight ratio of up to 133:1, scramjets about 2:1. So an equivalent rocket is up to 66 times lighter than a scramjet.
GE's patent refers to the use of a small amount of hydrazine in a catalyst-like role, or more accurately to act as a fuel/air mixer.
In addition to it's use as a monopropellant, hydrazine has been used as a fuel in bipropellant combinations, for example in a 30% by weight mix with 57% methanol and 13% water, with concentrated hydrogen peroxide as the oxidiser in the Messerschmitt Me163 rocket propelled interceptor. This suggests that it's use as a fuel in a scramjet engine might be technically possible, although it is chemically unstable and toxic in pure form.