A little deviation related to the theoretical aspects.

Having the opportunity to read the theoretical development of the Appendix 1 of the quoted article, an engineer would find as quite cryptic the academic work of von Karman, Vigness, Rodabaugh and George. I think a more accessible explanation (unfortunately the model there does not consider pressure but only bending) can be found in an excellent book- "Advanced strength of materials"- Den Hartog.

Basically the key in understanding what model considered are the sentences "there exists a means for the fibers to [partially] escape being extended and compressed" and "this requires the pipe to swell sidewise and acquire an ellipse-like cross section"- I quoted from subchapter 34, "Bending of thin-walled Curved tubes".
The method is counting the total energy stored in pipe and applying "the Theorem of Least work". They are a lot of approximations made in theoretical development and Den Hartog’s book does a good job explaining them.

It should be noted that Rodabaugh and George made a great improvement by counting the cumulative effects of bending and pressure, but the calculation principles remain the same.

Turning now the discussion to other theoretical aspect, the "rotational Bourdon" theory presents a different model that is validated under some circumstances and has also practical applications. The section is initially rather flattened and we count a new equilibrium, bend shape and cross-section shape; this could be done counting again the total energy stored and eventually predicting effects as displacements and rotation of the "free end".

I would say that these two theoretical models have some connections –maybe despite the common engineering perception- but they are developed in different mathematical ways under different assumptions.
Would both effects be considered for practical applications? In my opinion no; without entering in more details, my point is that an energetic approach of the model cannot count in two ways the total energy in pipe by giving two related consequences for calculation; better said, such effects wouldn't be superimposed. Eventually we have unique pipe energy associated with M and p and the effect of this energy is unique.

For this theoretical reason, taking into account the fact experiences (and Codes) validated the works of Rodabaugh & George, I can see no theoretical reason to consider "pressure stiffening in bends" together with "rotational Bourdon".