There are a number of references to Dark Sun natives on the planes in Planescape. There's a neighborhood in Sigil's Hive Ward called New Tyr (Faction War mentions that the inhabitants have a grudge against githyanki and githzerai; and yes, it's explicitly named after Athas's free city of Tyr, from which most of the locals emigrated, not the Norse/Forgotten Realms god). Another Sigilian neighborhood, Curly-Foot, was briefly inhabited by Athasian halflings until the non-Athasian halflings expelled them a few years ago; they may have moved to New Tyr by now, or they may have moved on to another plane. Planes of Chaos mentions Athasian elves have found their way to Pelion, Arborea's third (desert-like) layer. The Planescape Monstrous Compendium Appendix III includes two planar monsters that originated in the Dark Sun setting, the psurlon and the ruvoka. The psurlon entry doesn't mention Athas (they seem more concerned with contending with the githyanki for dominance of the Astral), but the ruvoka entry does mention that many ruvokas were once Athasian druids. The Dragon Kings hardcover for high level Dark Sun campaigns presented the standard planar map (from the 1st edition Manual of the Planes, the most up-to-date source when that book was published) for Athas, though later Dark Sun products muddied the picture by giving Athas its own unique paraelemental planes. The Inner Planes sourcebook for Planescape attempted to present those variant planes as just alternate names for the standard paraelemental and quasielemental planes, though vaguely, noting the location of portals and vortices between the standard inner planes and Athas. A Guide to the Ethereal Plane by Bruce Cordell informed us that Athas's Gray was a variant Border Ethereal Plane and presented rules for getting in and out of it, and the chances of getting lost.
Pirates of Gith could get to Athas via the Astral Plane, though the Gray would give them trouble. It doesn't necessarily "break" the setting to provide ways to crossover into other settings, although making it too easy might unbalance the economy by providing sources of metal and water that aren't supposed to be common on Athas, and might dilute the flavor of the setting in other ways. Probably most people who want to run a Dark Sun campaign want to run a game about gritty survival against hostile elements and despotic sorcerer-kings, not a free-for-all where they might randomly bump into lost kender and giff and hop a portal to the Forgotten Realms for a vacation on the shore of the Sea of Fallen Stars whenever things get too gritty at home. But for a Planescape or Spelljammer campaign that's already about hopping from world to world, yeah, it's possible for one of those worlds to be Athas, and this kind of travel is arguably sanctioned in various 2nd edition sources. Not that you need official sanction to do whatever you want in your game. In an Athas-centered campaign, it might make more sense to have portals only connect to planes that fit the theme of the campaign and the cosmology you've established for it; the Elemental Planes, Athas's distinctive Para-Elemental Planes, the Gray, and the Black would all be perfectly fine additions, and weird adventures involving trips to parallel versions of Athas where history went differently, or maybe a trip to the Dark Sun-inspired domain of Kalidnay in the Ravenloft setting, or new planes and new worlds that involved psionic creatures and survival in hostile terrain would fit the themes of a Dark Sun campaign organically, without feeling too jarring in campaigns that sought to present a consistent tone.
Way back in high school I planned out a world-hopping campaign in which Dark Sun's sorcerer-kings would turn out to belong to an interplanar society of wizards that would bedevil the PCs on multiple worlds as they all sought to locate pieces of an artifact scattered across the planes.