No. The Thief's Downfall only removes "magical concealment".
Whilst it's impossible to be definitive I think it's highly likely that the Thief's Downfall wouldn't have worked on Hermione's teeth.
The Thief's Downfall successfully erased Ron's disguise. But I think it wouldn't have effected Hermione. The difference, I believe, is that Hermione's teeth shrinking was a medicinal procedure rather than a purely cosmetic alteration. The Thief's Downfall deals primarily with spells of concealment.
"The Thief's Downfall!" said Griphook, clambering to his feet and looking back at the deluge on to the tracks, which Harry knew, now, had been more than water. "It washes away all enchantment, all magical concealment! They know there are imposters in Gringotts, they have set off defences against us!"
(Deathly Hallows, Chapter 26, Gringotts).
Ron's disguise was surface-level and temporary.
Hermione sighed and set to work, muttering under her breath as she transformed various aspects of Ron's appearance. He was to be given a completely fake identity, and they were trusting to the malevolent aura cast by Bellatrix to protect him.
(Deathly Hallows, Chapter 26, Gringotts).
The procedure Madame Pomfrey used on Hermione seems to be much more long-lasting. The shrinking spell was presumably designed to be permanent, after all.
"Hermione," said Ron, looking sideways at her, suddenly frowning, "your teeth..."
"What about them?" she said.
"Well, they're different...I've just noticed..."
"Of course they are - did you expect me to keep those fangs Malfoy gave me?"
"No, I mean, they're different to how they were before he put that hex on you...they're all...straight and - and normal-sized."
Hermione suddenly smiled very mischievously, and Harry noticed it too: it was a very different smile to the one he remembered.
"Well...when I went up to Madame Pomfrey to get them shrunk, she held up a mirror, and told me to stop her when they were back to how they normally were," she said. "And I just...let her carry on a bit." She smiled even more widely.
(Goblet of Fire, Chapter 23, The Yule Ball).
Madame Pomfrey is a skilled magical physician. Her treatments have to be able to withstand the 'rough and tumble' of the magical world. They wouldn't be effective if they were subject to alterations by spells like the Thief's Downfall. I think that Madame Pomfrey's spells are durable enough to stand the test of time.
Even if they aren't, Griphook says that the Thief's Downfall is designed to uncover "magical concealment". Ron's disguise was an attempt to conceal himself. Hermione's teeth shrinking was not. I think that the Thief's Downfall can tell the difference between the two and only shows the subject as they usually are, whether that normal state has magical alterations or not.