Telomere dysfunction plays a complex role in tumorigenesis. While dysfunctional telomeres can block the proliferation of incipient cancer clones by inducing replicative senescence, fusion of dysfunctional telomeres can drive genome instability and oncogenic genomic rearrangements. Therefore, it is important to define the regulatory pathways that guide these opposing effects. Recent work has shown that the autophagy pathway regulates both senescence and genome instability in various contexts. Here, we apply models of acute telomere dysfunction to determine whether autophagy modulates the resulting genome instability and senescence responses. While telomere dysfunction rapidly induces autophagic flux in human fibroblast cell lines, inhibition of the autophagy pathway does not have a significant impact upon the transition to senescence, in contrast to what has previously been reported for oncogene-induced senescence. Our results suggest that this difference may be explained by disparities in the development of the senescence-associated secretory phenotype. We also show that chromosome fusions induced by telomere dysfunction are comparable in autophagy-proficient and autophagy-deficient cells. Altogether, our results highlight the complexity of the senescence-autophagy interface and indicate that autophagy induction is unlikely to play a significant role in telomere dysfunction-driven senescence and chromosome fusions.