Yes, it can be modeled. You can calculate pressure drop vs flow rate through pipe for any Newtonian fluid, gas or liquid, using a Moody chart (search the term). However, that calculation only works for steady state flow. Your application will only have steady state flow at extremely low speed.
At any speed over about 10 to 100 RPM, a flow calculation will need to include the time to move the valve from closed to open, the volume of the tube, and the position of the piston. I once wrote a simulation for a high speed air cylinder. That simulation accurately predicted acceleration, deceleration, and presence/absence of bouncing. The simulation treated the valve as a variable orifice, and the connecting tube as a dead volume lumped with the piston position. Your case has a very long tube, which adds a complicating factor.
I suggest start with simplifying assumptions:
1) Valve opens instantly.
2) Piston at TDC, not moving.
3) Ignore pressure drop down the length of the tube.
4) Valve starts to open at TDC.
5) Ignore the speed of sound in the steam.
Then the only pressure drop in the system is the ##C_V## or equivalent orifice area of the valve. Then you can calculate the initial flow rate through the valve. Calculate the time for the downstream pressure to increase about 10%, then recalculate the flow rate at that time step until downstream pressure is almost equal to supply pressure. This can be done with a spreadsheet.
When you get that iterative calculation working, it's easy to add sophistication. Based on your results, decide which simplifying assumption you want to remove. If, for example, the time to fill the tube with steam is about equal to the valve opening time, that would be a good variable to add to your model.
IMPORTANT: Start as simple as possible, then add only one variable at a time.
