Rrerku

Can anyone confirm whether Section 31 ever appeared in a Star Trek: The Next Generation episode?

They did not. The organisation was invented for the DS9 episode Inquisition, broadcast 4 years after the last episode of TNG.

Q. Was there any debate about whether or not to establish that [Section 31,
in "Inquisition"] has been around for so long?

A. We had extended conversations about the backstory to Section 31 and yes, there was a lot of debate about how long and under what
circumstances this branch had existed.

_{^{Ronald D. Moore - Webchat AOL}}

That being said, Section 31 comes into conflict with the crew of the TNG Enterprise a few years after Nemesis in the EU novel Star Trek: Section 31: Control.

Data felt great pride at the progress his daughter had made in so
short a time. When he was her age, he had still been struggling to
master basic interactions with organic sentient beings. By contrast,
Lal meshed easily with organic beings, and in spite of what Data had
originally considered her fragile emotional state, she was
demonstrating tremendous calm and poise in the face of a serious and
perhaps even existential threat from Section 31.

As @Valorum already stated, 'Section 31' as a department was thought up during DS9's run, but in-universe the organisation, or specifically the article in the Starfleet charter that lends its name to the covert-ops branch, has existed since the very beginning. Here's a quote from the Star trek: Enterprise episode Divergence, where Phlox is ... involuntarily re-assigned.

ARCHER: Phlox was kidnapped. Starfleet would never authorise that.

HARRIS [on monitor]: Reread the Charter, Article 14, Section 31. There are a few lines that make allowances for bending the rules during times of extraordinary threat.

http://www.chakoteya.net/Enterprise/92.htm