Yes, Deadpool is inherently part of the X-Men universe based solely on the fact that he is a mutant and shares similar enemies, characters, and storylines with them.
This is obvious in Deadpool 2 when Wade (Ryan Reynolds) moves into the X-Mansion and becomes a trainee of the famous mutant-based team. He exchanges witty banter with Colossus (Stefan Kapičić), Negasonic Teenage Warheard (Brianna Hildebrand), and Yukio (Shioli Kutsuna) and even manages to get Professor X (James McAvoy), Hank McCoy (Nicholas Hoult), Quicksilver (Evan Peters), Cyclops (Tye Sheridan), Storm (Alexandra Shipp), and Nightcrawler (Kodi Smit-McPhee) to show their faces.
All of these references to the X-Men Cinematic Universe are very on-the-nose, but you might not know just how far the production went to entrench itself into this X-centric reality. Based on what we learned from the sequel's digital release on iTunes, everyone went the extra mile, whether it was for the biggest set pieces or the smallest gags.
Let's start at the end when Deadpool uses Cable's time travel device to go back in time and kill what is essentially himself from X-Men Origins: Wolverine. To achieve this hilarious bit of time-sliding skullduggery, the production got its hands on the actual dailies from Origins so that they could lengthen Hugh Jackman's close-up reactions, revealed Deadpool 2 director David Leitch on the audio commentary.
Going back to the beginning, let's talk about that amazing Logan music box that Wade turns on before blowing himself up. The little toy shows Wolverine impaled on the spike of wood that finally kills him at the end of James Mangold's Logan. When the Deadpool 2 commentary was being recorded (about three weeks before the movie's theatrical release), Mangold had not yet seen the music box moment, and apparently he didn't get a say on its inclusion in the film. Still, it's such a cool prop that Ryan Reynolds claimed he stole it after filming that day.
When it came to the X-Mansion, it was the actual home in British Columbia used for the filming of X2: X-Men United in 2003. Leitch explained that they were just going to use it for exterior shots, but he loved the inside so much that it escalated into a full interior shoot. And that Cerebro Wade screws around with when Colossus comes to get him for his first mission? Yeah, that was an actual Cerebro prop from the X-Men movie archives. To make things even sweeter, Wade breaking it was a real-life accident by Ryan Reynolds.
When Wade dies at the end (just like he promised Wolverine he'd do from the very start), his continual dying fake-outs were inspired by Bill Murray's performance in Zombieland, which Rhett Reese and Paul Wernick also wrote. Not only that, but if you listen closely, you can hear some of Marco Beltrami's death score from the finale of Logan.