Andrew,
If you constrain the thread you will overstiffen and the rotation about theta (cylindrical csys z-axis along the cylinder axis) will reduce.
This will push the high stresses along to somewhere else; more work has to be done in the structure elsewhere. i.e. 'bulging' under pressure should begin along the thread otherwise the answers are wrong and you will find that the stresses in any undercut are even bigger.
Also, if the threaded cap is loaded there will be a bursting force due to the angle of the thread. This radial load cannot be ignored. (butress threads attempt to mitigate this issue).
Weighted links can help but do not cause the bursting load. You could apply an estimate of the radial load I suppose.
For speed there are compromises each with criticisms. We tend to model 3 turns of thread at start-middle-end, simple triangles, keep the cap simple, use contact, assume pressure leaks into the first 2 turns.
Regards
Charles