But...apparently not. In at least one person's case.
Autobiography Chesterton Chapter XI
One amusing part of it is what he refers to as "the great battle of the Beaconsfield War Memorial." Here is a very small excerpt:
There was a sequel, however, involving more serious things. A renewed shock went through the anti-clerical party on finding that the Cross was a Crucifix. This represented, to many amiable and professedly moderate Nonconformists and other Protestants, exactly that extra touch that they could not tolerate. The distinction is all the more clearly to be kept in mind because it is, on the face of it, an entirely irrational distinction. The sort of Evangelical who demands what he calls a Living Christ must surely find it difficult to reconcile with his religion an indifference to a Dying Christ; but anyhow one would think he would prefer it to a Dead Cross. To salute the Cross in that sense is literally to bow down to wood and stone; since it is only an image in stone of something that was made of wood. It is surely less idolatrous to salute the Incarnate God or His image; and the case is further complicated by the relation of the image to the other object. If a man were ready to wreck every statue of Julius Caesar, but also ready to kiss the sword that killed him, he would be liable to be misunderstood as an ardent admirer of Caesar. If a man hated to have a portrait of Charles the First, but rubbed his hands with joy at the sight of the axe that beheaded him, he would have himself to blame if he were regarded rather as a Roundhead than a Royalist. And to permit a picture of the engine of execution, while forbidding a picture of the victim, is just as strange and sinister in the case of Christ as in that of Caesar. And this illustrates something about the whole situation, which grew clearer and clearer to me about this time and initiated the next step of my life.
As you can surmise Chesterton was not yet a Catholic.