The short answer
Yes, with early starts. May and September are the shoulder months: hot at midday but fine at sunrise and sunset, with quieter dunes than spring. Our Sahara guide puts May middays creeping towards 35 °C and September at about 35 to 40 °C, easing sharply in the second half. Keep outdoor time to the cool ends of the day.
In more detail
Most camps run as normal in May, and the spring crowds have thinned. The rose season in the Dadès valley, on the road to Merzouga, falls in May too, which makes for a good drive. Plan the camel ride for late afternoon and the dune climb for sunrise, and spend the middle of the day in shade.
September is the reverse: the worst of the summer has broken but it is still hot, and the second half of the month is much better than the first. If you have a choice, aim for late September, or wait for October, when the season proper begins.
In both months, nights are mild rather than cold, so you need lighter layers than in winter. Drink more than you think you need on the drive, and choose a camp with shade and, ideally, cooled tents.