The short answer
No. The road from Marrakech to Merzouga is paved all the way to the edge of Erg Chebbi, and a normal car handles it. A 4x4 is only needed for the drive across the sand into some camps, which the camp provides, and for the piste from M'Hamid to Erg Chigaga, which is a different desert.
In more detail
The route runs on the N9 over the Tizi n'Tichka to Ouarzazate, then east on the N10 through the gorges to Erfoud and Merzouga. Our guides describe it as paved throughout and in reasonable condition, with the mountain switchbacks the only demanding part.
Where a 4x4 matters is the last few minutes into the dunes. If you do not ride a camel to camp, the camp brings you in by 4x4 from where the road ends. Your own car stays parked at the edge.
Erg Chigaga is the exception. The tarmac stops at M'Hamid el Ghizlane, and the dunes lie across open hammada on a sandy, unpaved track that needs a high-clearance 4x4 and a driver who knows it. We provide both on Chigaga trips. A 4x4 is still a comfortable choice for Merzouga, with room for luggage, but there it is a choice, not a need.