Study what difficulties Leica has had with their short-flange lens mount and that gives you an idea.
In short, when a ray of light hits the film plane in a steep angle (steepens near the edge of the image circle), the film and its optical properties do the right thing, directing light perpendicular. A digital sensor is all about transparent pieces of glass (microlenses) that have their usual (back)reflective properties: the light hits the microlens in a bad way, some of it will scatter around. There's a great clip from a Kodak engineer giving a talk on this subject, from early 2000s or late 1990s but can't find it on Youtube right now. :/
Many other brands didn't have as much problems with their legacy lenses but that's because they were SLR bodies, larger bodies with deeper flange distances. Nikon F, Canon FD, EF from the 80s all were suitable for digital work. (Of course some of the Nikon F-mount or Canon FD-mount bodies are positively compact, so is my theory off?)
If we're talking about compact cameras like a Ricoh-something from the 90s or Nikon 35-Ti, they have nice compact bodies and positively cutesy lenses on them. Mighty sharp as well. They would be more difficult to build as digital 35mm equivalents. The lenses are sharp for film but they'd probably not satisfy pixel peepers of digital folks. The steep angle requires some bad magic on the sensor and probably tough design on the lens. All making it very unlikely you could pull it off keeping the original dimensions.