Sure, you’re talking about Uncanny X-men #268, a retro teamup set in WW2 that still felt pretty 1990 thanks to more than the usual amount of ninja. This is a Claremont/Lee joint, the gruff Wolverine and young and idealistic Captain America team up to save a little girl from the Hand. Also Nazis.
Strucker: I’m given to understand— by the old man who leads these costumed fanatics— that young Natasha here has an extraordinary aptitude for the martial arts. Under his tutelage, he will become the Hand’s master assassin.
It was 1941, and Ivan was living from place to place, Natasha in tow, trying to keep her safe from the Hand. Logan was hunting the Hand, Steve was hunting Nazis— together again, for the first time! As to whether or not it’s still in continuity, well—
Jubilee: Her? That old?? Uh-uh. Now way not a chance totally impossible! They’re talking like ancient history!
Uncanny X-men #268 was the first comic to suggest that Natasha was way, way older than she looked. The connection to World War II wasn’t new— in the earliest tellings of Natasha’s early life, she was a Russian war orphan adopted by the soldier Ivan Bezukhov. (I suspect this was all kind of a shout-out to Modesty Blaise.) But that version of her backstory, complete with the Battle of Stalingrad, was established in the early 1970s. Back then, it stuck Natasha in her mid-thirties. In 1990, it made her close to sixty. The issue offered no explanation, and if Claremont had one, he left the book before he could reveal it.
Because she’d only been secretly immortal in one comic from 1990 with absolutely zero rhyme or reason other writers gradually ignored that one comic, and if it wasn’t explicitly retconned it was definitely ignored. When Devin Grayson wrote her 1999 Black Widow mini she pictured Natasha as a creature of the Brezhnev era, and Richard Morgan had his Natasha approaching her fortieth birthday in 2005, not her 70th. These sorts of timelines made Uncanny #268 impossible, and that sort of non-retcon is pretty standard in comics. Reed Richards had World War II adventures, too, those have gradually fallen out of continuity because it makes no sense to acknowledge them.
But, in 2007 Ed Brubaker brought the “Black Widow doesn’t age” idea right back, so that he could retcon in a 1950s romance with his Winter Soldier pet project. Around the same time, Daniel Way did an Uncanny #268 flashback of his own in Wolverine Origins #16, but we don’t talk about that here. Basically, though, the World War II stories were back, and Paul Cornell and Marjorie Liu both worked to make Natasha’s agelessness part her own sombre character instead of just an excuse for cool retroactive team-ups starring dudes.
TL;DR: yes that story is still in continuity.
As for Natasha’s relationship with Logan, the punchline of Uncanny X-men #268 was that Natasha was the first Kitty Pryde, the first of many spunky little-girl sidekicks the man seems to acquire. For this reason it’s kinda creepy that fandom often assumes they’ve slept together. Logan was too transient back then to be a real fixture, a constant influence— it was Ivan who raised her, who was always there, not Wolverine. But when Wolverine was there he was being kicking rad and punching ninjas in the face, so of course he made a strong impression.
I’m not sure I’d call them close, exactly. Natasha doesn’t have the same kind of melancholy heart-to-hearts with Logan as she does with Matt, for example. I’m not sure he’s #1 on the list of persons she’d bare her soul to. But she doesn’t need to, with him, there’s a kind of weary trust there instead, borne of cruel lives that have crossed paths for decades. Logan respects the woman she’s become, but is still perhaps a touch overprotective. He remembers, now, the little girl she used to be. Natasha allows it, maybe because it’s nice that someone does.