I know that "signora" is, in Italian, the title for a married woman... But, would Italians refer to a married American or otherwise foreign visitor as such?
Signora is not the title of a married woman (anymore). Nowadays it is the courtesy title for any woman whatsoever. It would be used any time the speaker would need to address a woman they are not familiar with, irrespective of the marital status or country of provenance.
PS: I know that some people still use signorina for unmarried ladies, but I do consider it extremely disrespectful and I know several women that agree with me on that. Use it at your own risk and peril.
Since my post is garnering a few downvotes (I assume regarding my postscriptum), let me add a small note from the Accademia della Crusca, regarding the differing usage of signora and signorina (my translation):
The asymmetry between masculine and feminine forms has been considered sexist and, at least starting from the early eighties, the usage of signorina to refer to an unmarried woman has been more and more advised against. [...]
Today the acceptance of the term signorina by the concerned individuals is rather oscillating. There are still (although a lot less than in the past) some older unmarried women that, when adressed with signora, correct the allocutive with no, signorina; signorina prego or similar expressions, as well as young women that, upon being called signora, or seeing their name prefixed with signora, are surprised (it is the case of students during the graduation ceremony, at the moment of the proclamazione) or, as one of our readers signals, get offended, as if they were called old. On the other hand there are also young women perceiving the allocutive signorina almost as an insult: I remember seeing it in television during 2015 in a couple of occasions the honorable Pina Picierno, from the Partito Democratico, react violently after the Lega Nord politician Matteo Salvini called her signorina (the reaction: «Signorina lo dici a tua sorella!» «Call your sister signorina!»).
As you can see there are strongly diverging opinions. I personally always recommend when in doubt to err on the side of more formality, and so to use signora unless explicitly asked by the other party.
Yes, they would.
Signora is the formal way of addressing a woman, in oral and written form, regardless of her citizenship or spoken language, as appellation or as allocative (see below).
In some formal occasions it is still made the difference between signora, for a married woman, and signorina for a not married one.
In Parliament, e.g., by law a not married woman should still be addressed as "Signorina" even if it is sometime allowed the use of "Signora".
In the everyday life it should be offensive to refer to a not married woman on her 30s as Signora (you are telling her "old woman"), as to refer to a not young one as Signorina (you are telling her "spinster").
It is more a question of education, of tact or even of political beliefs than of Italian language; both words exist and have been in use since the 16th century.
Moreover, signora is still the title of a married woman
"Il signor XXX e la sua signora"
...and what you find in the forms to fill out.
Il/La sottoscritto/a sig./sig.ra , nato/a a
Some words more
We can read from an article from the "Accademia della Crusca" 
Signore, signora e signorina possono essere usati sia come appellativi, per indicare persone presenti o di cui si sta parlando, sia come allocutivi, per rivolgersi a qualcuno. In entrambi i casi si tratta... di forme di riguardo.
which can be translated into English
Signore, signora and signorina can be used both as appellations, to indicate people present or of whom one is speaking, and as an allocative, to address someone. In both cases ... it concerns forms of regard.