Are Naga tomes a legitimate threat to Dragon Emblem?

yes, correctly built Naga tomes are a very hard to dragon emblem.
that being said, its rare to see a Naga tome, and even rarer to see one correctly built.

this is coming from a Naga tome user, not a dragon emblem user, btw.

Probably the goto build for Deirdre to counter Dragons

Not really. Julia and Deirdre are slow so they probably don't even outspeed any dragon in the game.
Falchion user tho. Watch out for those suckers. Especially Exalted Chrom and L!Marth. Those boys hit hard.

H!Myrrh at 32 Res and color advantage still gets chunked by Naga tomes. I'd say they're dangerous, however, they're extremely rare in AR and Arena. You're more likely to face more Falchion users than Naga users.

I feel like naga tomes became a no-threat when the weapon refines where introduced.

Since the naga holders have middling speed, terrible def, but great res, they used to be able to fight dragons and take little damage. Now its not a guarantee that they will survive the encounter, or even do enough damage to win the encounter.

If the only red on a dragon team is an A.Tiki slow enough to get doubled, or if the Naga tome has high atk, I think definitely yes. F.Grima and blues can definitely die in one hit; F.Kana can die in one hit; F.Azurcorrin can die in one hit; some versions of M.Grima can die in one hit, especially unmerged versions.