If the intake has been sized to match engine requirements in subsonic cruise then it will be too big for the engine at Mach 1~1.2 ish. That will mean that excess airflow has to be spilled out of the front and the intake will develop a strong normal shock which stands off the intake LE. Flow behind that shock would be subsonic everywhere so there would be no shocks inside the intake itself. In effect it becomes a subsonic intake operating behind a shock wave that transforms the oncoming supersonic flow into something the intake can handle, albeit with significant loss of total pressure and increased drag.
So far as I can see, the same is true of the pitot intakes used on early fighters, but because of the sharper leading edges the bow shock wave would be weaker.