Could sacroiliac pain radiate to the lower abdomen?

Not typically: I've never heard of a case of sacroiliac joint pain referring to the lower abdomen. The best way to find out is to get the joint injected under x-ray with steroid and numbing medicine and see if the lower abdomen pain goes away too. Better yet, you can just get the L5 dorsal prim ramus, and s1, s2, (racepinephrine) s3 lateral branch nerves numbed up. An interventional spine specialist will know what this means.