Yes, there is some element of fraudulence here, but I believe the English word "faint" conveys relatively the same idea. غش کردن here has a figurative meaning, something like "dying for". Maybe we could also say "I die for the same Qibla toward which you stand to say a prayer." Nevertheless, I believe whether or not fraudulence or pretendence is involved, the form of expression must not change.

Persian (Farsi) term (edited): it ud'

to be cut from the same cloth

This is pretty much the literal meaning here and indeed is what the speaker means to say.

However, the overall meaning of the text is extremely culturally bound.

The speaker is swearing by exaggerating his own religiosity to show how much he is on the Hajji's side. Instead of simply saying he prays like Hajji (that is, kneeling سجده کردن to say his "namaz") he says that he "collapses or swoons" when facing the "ghebleh"

There is really no easy comparison to anything Christian, but something like this can give an idea: "by the same altar you kneel at, I fall and prostate myself..."



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Note added at 1 day7 hrs (2013-01-19 20:05:47 GMT)
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No, it is not like your suggested interpretation...as I understand it, the speaker is simply swearing by the same "ghebleh" that Hajji faces but he is emphasizing/exaggerating it by saying that he "swoons/collapses" when he does it.

Another analogy: you say "I swear on the Bible" and I say "I swear on ten Bibles, cross my heart and hope to die"