If I apply a displacement to a node, is there any way to find out what load is being applied to the model to achieve this displacement?

Sure.
Give a Force (iterativ) at this node.
Look the result displacement on this node.
If the result displacement equal you input displacement, then you have the right force.

... and start with the reaction force you obtained at the location of the displacement.

There is no reaction force at the node. I checked the 'restraints extended' ouput and there is a displacement reaction at the node, but no forces only bending moment. There is no restraint on the node that the displacment is applied to.

Check the FY reaction at node 40 in this model.

Reaction force is not the right word.
Reaction moments and force becomes only on this nodes you have a restraint.
But you become element force and moments (inner values).
Richard mean.. check the element force at the same coordinate as your displacement are.

I cannot download the file, it takes me to 'page cannot be found'. I will investigate element forces further and try an iterative approach...

Just build a cantilever model. At the free end displace it down 1 inch. Observe the magnitude of the "displacement reaction" in the restraint report.

Go back to the model, remove the displacement and apply the observed reaction as a force at the free end.

Ok, I'll give that a try. Its a rotational displacement that I am applying, to investigate the effect of misalignment of 5degrees on a flange.

Roger
the applied load at a point displacement / rotation acts only on the degrees of freedom restrained, ie. a rotation is imposed by a moment. But this also causes displacement (check your output), so to keep the flange in position a displacement fixity is also required.
This sort of analysis starts to get tricky if you want to see what happens when the pipe is operating.. 5 degrees is a big rotation btw.