On a crusier that was riding in straight lines...sure I'd rock old tires. Strafing apexes on a 150 hp sportbike and dragging knees? No thanks.
I'd assume the rubber has deteriorated and when safety is on the line I wouldn't wanna assume the tires would grip....however, while riding in straight lines you are asking so little of the tires as far as traction goes, I would. But bear in mind that your grip while braking may be diminished as well. Again, if riding an 800 lb crusier with a single front disc brake, I'd bet the tire grip isn't the limiting factor in braking efficiency,LOL