In principle, it should be possible to use existing sense-annotated data to explore this question: almost all sense annotation efforts have allowed annotators to assign multiple senses to a single occurrence, and the distribution of these sense labels should indicate whether annotators viewed the senses as disjoint or not.
the percentage of markables that received multiple sense labels in existing corpora is small, and it varies massively between corpora: In the SemCor corpus (Landes et al., 1998), only 0.3% of all markables received multiple sense labels.