I'd actually think this would be more plausible if the revolution established some sort of neutral democracy (because let's assume the Soviets are super-distracted with something else and are going through an internal crisis too, just to add fuel to the fire), and then all the Horthyist officers and Arrow Cross boys came out of the woodwork and made the coup happen. That would lead to a rather interesting situation... but it'd require a ~1945 POD. The old Horthyist military command was purged very thoroughly after the war (everyone who didn't actively sabotage the old regime somehow was removed at the very least, and the new authorities required very little evidence to imprison officers for anti-state activity), and there were no Horthyists left in the military by 1956. There were Horthyists trying to conduct espionage, who were mostly based in Austria and cooperated with various Western intelligence agencies, such as the kopjások ("lancers") and the MHBK ("Alliance of Hungarian Brothers-in-arms", translated loosely), but they never accomplished much and many of their members in Hungary were arrested due to the work of double agents. There was nobody who could have done this in 1956 IOTL.