No, Insidious and The Conjuring are not connected in-universe. That said, many crew members worked on both the original Insidious movie in 2010 and the first The Conjuring movie in 2013. The main reason for that is likely due to the fact that James Wan directed both films. In fact, Wan was approached about doing The Conjuring because of the success of Insidious. Wan was hesitant to do another ghost movie, but, since Insidious is not based on a true story, he was interested in directing a movie based on real people like Ed and Lorraine Warren. Another connection between the Insidious and Conjuring universes is, of course, Patrick Wilson who stars in both franchises.