As said above, the Centre Party had some big stakes in and supported the Reichsbanner. There were also some ties to the Stahlhelm veterans organisation, though small and not very strong.
If there would be an own Centre party - catholic paramilitary organisation, problem for the Weimar Republik would be : even more defragmentation and chaos. With its large and firm supporting base in the catholic regions it woudn't have too much problems regarding 'recruiting' and I could envisage it in size of about 150.000 to 200.000 (at the utmost, the lesser more realistic IMO). But this would - to some extent - on cost of the Reichsbanner. Still a large force, mainly operating in the catholic regions (Ruhr, Rheinland, Silesia, ... not so sure of Swabia/Wuerttemberg and Badenia, much 'older' nationalistic Freecorps-regions).
And there only adding to civil-war like conditions.
IMO that would make a Reichswehr/Schleicher take-over much more possible earlier on.
However, the Centre party lacked one important factor to support the build-up of such an own paramilitary 'streetfighter'-wing : ideology of FIGHT as part of (almost) daily life as well as global life.
No need (IMO) to point out the role of 'fighting' in the right-wingers ideologies. The left-wingers 'grew' up in the ideology of 'class-fight' everywhere in daily like as well as on global/international scale.
But christian ideology, the very heart of the Centre party favors a unifying, forgiving stance looking for compromise with others instead of crushing others. Their 'hero' is the Martyr instaed of the Victor.
But if - for some (ASB) reasons I have no idea of - such an organisation ight come into existence :
what about "Crusaders" ? or "The true (believers)" ?