A metal‐free radical multicomponent bicyclization of heteroatom‐linked 1,7‐diynes with aryl diazonium tetrafluoroborates and DABCO‐bis(sulfurdioxide) (DABSO) is reported, enabling annulative SO2 insertion access to produce two types of skeletally diverse tricyclic sulfones, namely, thieno[3,4‐c]quinoline 2,2‐dioxides and thieno[3,4‐c]chromene 2,2‐dioxides, with moderate to good yields by simply tuning the linkers of the 1,7‐diynes. This protocol demonstrates remarkable compatibility regarding N‐ and O‐linked 1,7‐diynes with different substitution patterns and aryl diazonium tetrafluoroborates.