"Such-and-such (a)" + singular noun

This is interesting, and there does seem to be divided usage. Google ngrams for such and such a street and such and such street (and a check on references given at the link) show that both are used (with various choices of hyphenation), the one containing the article 'a' being five times as common a choice.

This is probably because there is an attempt to conform to standard grammar, though logically 'such and such a' is no better than 'such and such' as a placeholder some would portray as _____ or XXXX.

Collins Cobuild does not analyse such and such more than to call the whole a phrase; when used before a noun, the near-equivalence of 'some' might make some argue for determiner classification. And Collins does not even comment on the fact that a is typically included before a noun. As seen below, the distribution of 'such and such [a]' is fairly wide, not merely prenominal:

such and such [phrase]:

You use such and such to refer to a thing or person when you do not want to be exact or precise. [spoken, vagueness]

• I said, 'Well what time'll I get to Leeds?' and he said such and such a time but I missed my connection.
• He'd like to give a course of lectures on such and such a topic.
• we went to such and such a place [from Webster's]
• Or that the friend you trusted was going to betray you in some way on such and such a date? [Anthony Masters: Cascades - The Day of the Dead]
• And so we produce masses of documented research to define a target audience in such and such a demographic. [Stuart Harrison: Better than This]

The last example is more unusual, as 'such and such [a]' is, as Collins adds, usually used in informal contexts.

[re-ordered]

Collins includes examples where 'such and such' is not used before a noun, and the 'a' is inappropriate:

• What if such and such had happened instead? [used ostensibly as a noun phrase]
• Father, forgive me for I have sinned, she said, my last confession was such and such ago. [Louise Erdrich: The Last Report on ...] [used ostensibly as a measure phrase]