Learn English – The meaning of the phrase “should they prove correct”

These repeated usages from the television series "Are you being served?" are probably a literary device to suggest that the speaker lacks education.

That said, this NGram shows that usage in written English is rare but has risen consistently since the 1850's apart from during the two world wars, and is more common in American English than British English.

Typically, stood functions as a verb in the sentence and standing is used to attach an adjective that describes the way in which the person is standing. Here is a typical example:

He stood standing still next to the oak tree, next to which Dronian was buried. Dreamweaver - Nicole Weisensee (2011)

Most instances are run of the mill fiction, but there is one notable exception- one John Keats, maybe exercising a bit of poetic licence:

Until he reach’d the great main cupola;
There stood standing fierce beneath, he stampt his foot,
And from the basements deep to the high towers
Jarr’d his own golden region Hyperion book 1 - John Keats (1820)

Note that stood has been edited out from some editions.

Both should and if express a degree of doubt. They both acknowledge the possibility that the person being addressed will not accept it. Should just comes across as slightly more formal.