No. Determining adequacy of design is outside the scope of a home inspection. As a home owner, I would not rely on IC rating. I have investigated several fires caused by IC rated fixtures. The placement of the thermal switch is critical and it can move during shipping or installation. We tested many different brands in our lab and found failures with every brand we tested. Moving the thermal switch as little as a couple of millimeters meant the difference between opening and not opening in some of the fixtures we tested.
As a side note, tracking (burning) of cellulose insulation can go on for days, weeks, or months before an actual fire starts. A fire may start many feet away from a recessed fixture. The fire will start where the tracking meets a fuel source and an adequate supply of oxygen. The actual fire almost never starts at the fixture.
As a home inspector, I gently run my hand through cellulose insulation around a representative number of recessed fixtures to see if there is tracking. Regardless of whether the fixtures are IC rated or there is tracking, I always recommend maintaining clearance around the fixture where there is cellulose insulation.