Image stabilisation is relevant mostly for countering the effects of small rotations around several axes. For the overall picture, the effect of those rotations is roughly proportional to the effective focal length (but for pixel peeping, the effect grows again with the resolution). For larger sensors, one tends to have more and longer glass for the same effective focal length which stabilises by its weight. However, holding large weights when not close to the body tends to cause more of an arm musculature tremor when not using at least a monopod.

I have an old DSC-R1 camera without image stabilisation, an APS-C class sensor (crop factor 1.67 I think), only 10MP of resolution and a maximum effective focal length of 120mm, at a weight of about 1kg. At speeds of about 1/5s you have a moderate amount of success with photographs given enough practice. You can add about 1.5kg for a teleconverter giving an effective reach of 200mm. Arm shake at this weight becomes an issue.

Basically for longer focal lengths foregoing image stabilisation with handheld shots is really going to become problematic in my experience. However, in contrast to my old camera, current large sensor offerings have large usable ISO ranges so you often can use exposure times short enough that image shake is not a significant problem, and as a side benefit object movement is then not a problem either.

So if you are leaning towards a camera without image stabilisation, have a very good look at its high ISO performance and maybe also about the ability to work with external lighting (like on-camera and off-camera flash).