Question tag for "many a ..."
Consider the sentence "Many a rose bloomed in the garden."
If you had to substitute "many a rose" with a pronoun, what would it be?
"Many a ..." takes a singular verb. Does that mean it can be substituted by the singular pronoun it?
If you had to add a question tag to "Many a rose bloomed in the garden", what would it be? Is "Many a rose bloomed in the garden, didn't it?" grammatical?
Here's what Bryan Garner, Garner's Modern American Usage, second edition (2003) says about the idiom "many a":
many a. This idiom requires a singular verb {many a new father has fretted about whether he is helping enough to care for the newborn}. Essentially, because the idiom is distributive rather than aggregate in sense, the verb is singular.
The complication in the OP's example is that the verb's number is buried in a simple past tense verb (bloomed) that applies equally to singular and plural subjects; and this in turn encourages writers to think that perhaps the subject in "Many a rose" isn't rose (singular) but Many (plural).
This line of thinking would be less likely to occur if the example used a verb form that exposed the number of the relevant verb. Here, if the choice were between "Many a rose has bloomed..." and "Many a rose have bloomed..." I think that most native English speakers familiar with the "many a" idiom would immediately choose the version with the singular verb:
Many a rose has bloomed in the garden.
But once you've taken that step, it hardly makes sense to adopt the plural pronoun they when referring to the subject. The mixed form sounds very odd:
Many a rose has bloomed in the garden, haven't they?
whereas the consistently singular form sounds normal:
Many a rose has bloomed in the garden, hasn't it?
Returning to the original example, with its two number-neutral verbs bloomed and didn't, I would apply the same reasoning as in the "has/have bloomed" instance, which logically yields this result:
Many a rose bloomed in the garden, didn't it?
The noun that completes the "many a" idiom can be anything countable—rose, man, one, etc.—but it is always singular; and in my view, it is the true subject of the idiomatic form.