I am not sure this helps clarify Frye’s enigmatic statement about the Vicar of Bray not becoming a bishop, but Craig Walker’s post led me to a piece entitled “The Analogy of Democracy” (1952).  There Frye argues that

 democracy is to be judged not by what it does, but by what it aims at in spite of what it does. The supremacy of civil over military power, the full publication of all acts of government, the toleration of unpopular opinion, are all recognized to be unchangeable principles of democracy even when they are flouted as often as exemplified. Further, any feature of democracy that is nothing more than a safeguard designed to prevent a democratic process from congealing at a certain stage in its development may disappear when democracy passes that stage. We may find that even such apparently essential things as a two-party system of parliamentary government may so disappear. On the other hand, the fact that democracy is not in itself a form of government makes it possible for it to adapt itself to a wide variety of such forms. If the United States decided to adopt a Soviet system or, as in Bernard Shaw’s The Apple Cart, to recognize George VI as their king, the move might be inadvisable, but it would not be in itself a threat to democracy.

[Pages 219-20 in Northrop Frye, Reading the World, Selected Writings, ed. Robert D. Denham, 1935-76, New York: Peter Lang, 1990; the essay was originally published in Bias 1 (Feb. 1952): 2-6.]

In the same essay Frye observes that

the ultimate aim of democracy is to reach what is not only natural society, but a secular analogy of Christianity. The church is a community whose members are made free and equal by their faith. It is ordered by its Master to take society as it finds it, to render to Caesar what is Caesar’s. This, of course, excludes the worship of Caesar as a divine being, which is one of the things that the Caesars of this world are most interested in, and Caesar finds other difficulties in trying to digest this free and equal community in his pyramidial state. To the extent that it obeys the command not to resist evil, the Church’s social dialectic works toward compelling the whole social order to fall into a pattern analogous to its own. This triumph of the Church in manifesting its Master’s victory over the world is the real meaning of the democratic revolution today. (224-5)

This seems to fit with what Craig Walker is alluding to in his citation of Bernard Shaw: the vicar of Bray most certainly takes society as he finds it and goes out of his way not to resist evil. However, Frye was very ambivalent when it came to Shaw, had a great distaste for his political and psychological fixations, such as his mother-fixation and his adolescent contempt for democracy and longing for a ruler. Frye may have been an avid Shaw reader when he was young, but references to him in his writing are often highly critical.

Frye elaborates the same idea in another essay in the same volume, “Preserving Human Values” (1961, transcribed from a talk given at the annual meeting of the Social Planning Committee of Metropolitan Toronto, 27 April 1961):

I imagine that our ultimate goals are not very different from those of our Communist rivals. I imagine that a classless society, a withering away of the state, are our own ideals as well. For democracy, if it is a goal and in part an ideal, is not a system of government like a republic or monarchy. If the United States were to adopt to a Soviet system, or if it were to swear allegiance to Queen Elizabeth as its Queen (as the Americans do in Bernard Shaw’s play, The Apple Cart), that might be an undesirable move, but it would not be in itself a threat to democracy. It will be too bad, I think, if democracy suffers from a sense of fixation about its own political machinery. It is possible that voting on grossly oversimplified issues for candidates who are controlled by political machines rather than by electors may be something that in time to come we shall decide is a bit expendable. (327)