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Steam will condense any time it is in a situation to lose enthalpy to something else. Next to a cool surface? It will condense to heat the surface. Sp if some steam could get to the infinitely small orifice location, yes some would condense on the pipe walls near the orifice. Exactly enough, in fact, to compensate for the heat loss of the pipe into the surrounding space.

But… this has nothing to do with whether the orifice is blocking steam or not. Exactly the same amount of steam would condense in that location and pipe if there were no orifice at all.

Or let's look at it in a more direct answer to your question as stated, which was "if the orifice were infinitely small (no hole), would the steam just stay hot for the duration of the heating cycle? Or would it condense, at least small amount, in the valve/piping," If the steam were present, and the supply piping were cooler than the steam, heat would transfer from the steam to the supply piping and the steam would condense.

Or take a third whack. Saturated steam is, by definition, water vapour in equilibrium with liquid water at the stated temperature and pressure. If any energy is extracted from the water vapour, that energy will come from condensation of some of the vapour in the form of liquid water.

I suggested it earlier, I will again: look up the definition of enthalpy, and then find a good thermodynamics textbook and study it to understand it, and then you will be on the way to understanding how the physics of heat transfer using combined vapour/liquid phase systems (of which steam heat is one — and so are heat pumps and refrigerators) works.

Short answer. No.