I would like to answer the main question: Can vehicular cyclists also advocate for bike lanes and paths? The answer is they already do, and yes, they should. (And to be clear, I mean vc, not VC(TM), cyclists because the Foresterites simply won't advocate for these things so they are irrelevant.)
Why should vehicular cyclists advocate for these things? Because they are the ones with the empiricle experience who understand the problems of poor design of traffic systems. They have expertise the engineers often lack. They are also the ones who will reject designs where the motivation is to "push cyclists out of the way". They are the true stakeholders in the system who can ensure lanes and paths don't hinder their mobility or inhibit access for others. When left to to motorists and people who ride on the sidewalk (as it may very well be in many areas) what gets built largely lacks utility.
I believe vc cyclists have a responsibility to be part of the process that advocates for lanes and paths. This means you offer what support you can: money, letters, votes, time, whatever.