I'm giving my original answer-turned-comment a re-makeover.
No. I don't see how a Catholic/Christian can be an anarchist. They may have some anarchic views I guess, and even do some anarchic stuff, but it seems to me that there must some presumed separation between 'this world' and 'the beyond' for this to jibe. Anarchy only fits for us mortals, of course, in the *former*, lesser world and then, only to a degree by decree, and in the *latter* only for Gawd prior to creation.
(I say this as one who uses the word 'anarchy' in the sense of movement, flux, process, becoming rather than a future 'state' of being.)
According to the mythology, Gawd is Bawss of both worlds, so the parameters of anarchy are set in stone tablets for us to follow, and following doesn't seem all that anarchic to me, especially when the choices are pared (or is that paired?) down to yes/no's like; follow or roast for eternity. IMO, fear simply isn't fertile ground for lives to flower forth in joy, beauty, and gratitude for this immediate moment. Fear promotes more misery.
Also, it seems to me that religion has always been a cohort of the State by way of normalizing hierarchical, dominating relationships while at the same time providing salve to cope with the very shitty circumstances it provides apologia for...AKA, morality. In sum: a state of consciousness in favor of, and protecting, the State of enforced conditions.
How one reconciles the flux and uncertainties of anarchy with a cosmic pyramid-scheme of lawn-order seems to involve some spectacular hermeneutical gymnastics in order to not anger the Queso Grande...but I'm all ears.
edit for clarity