Meaning of a sentence in The Man Who Was Thursday

Solution 1:

The problem is that, as it stands, the sentence simply doesn't make sense.

Not finding the professor out (penetrating his disguise or understanding his motives) wouldn't seem to be a particularly good thing. Equally, being found out by the professor would also seem to be a bad thing.

Removing the "not" in the first half of the sentence resolves the problem:

"It would be no help that he could discover the professor's identity, if by some serious accident the Professor should discover his identity."

Whatever Chesterton originally wrote, editorial intervention in some form on the part of the reader would seem to be necessary.

There's this, which may provide an explanation:

"The Man Who Was Thursday was published in February 1908 ... The unexpectedness of the book is perhaps the reason why both this and nearly all subsequent editions are marred by misprints."

The sentence as originally given may be a case of a misprint which has escaped later correction.

Solution 2:

The phrase "find him out" is idiomatically used to mean "discover his secret", in this case, his identity.

The phrase "very small comfort" is used to mean "no comfort at all", or "of no use" or "of no help". This is a litotes.

It would be no help that he could not discover the professor's identity, if by some serious accident the Professor should discover his identity.

That he cannot discover the professor's identity suggests that the concealment is possible, so may give him comfort. However the professor may nonetheless discover his identity by some accident. At that point, the fact that concealment is possible is of no help.