I wouldn't! It also depends on the type of neck dissection you had. A radical neck dissection, RND, bedsides removing the lymph nodes in levels II-V, also removes the neck muscle, vein and nerve, so there is no stability. Another factor is some have a weaker carotid artery from radiation and or surgery from manipulation or scraping the tumor off the artery, and I had alloderm to put over to protect it, due to no neck muscle, and more recently a pec flap, whereby the alloderm was peeked off.

A few months ago, while going home in car service from the doctor, the driver stopped suddenly, jerking my head forward and backward, and immediately felt a jolt in my neck where I had three neck dissections. It got worse later on, and could not turn my head at all. This lasted well over a month, and was worried of any damage to my neck, and can imagine what a roller coaster ride may do.

Maybe ask your ENT.