Does it swivel from left to right while in the recumbent position?

Yes you can but not recommended.
Our recommendation:
Be sure bed is on a level, non-slippery surface.
Be sure to adjust self-leveling feet.
Always orient the bed in-line or parallel with the base for treatment purposes.
When rotating the bed, it is recommended that there be no client on the bed at that time.
If there is a client on the bed during rotation, it is recommended that client be seated in the upright sitting position.
When rotating the bed, if there is a client in the bed, the bed MUST be held from underneath at the head of the bed by the operator as it is in rotation.
Sitting on either the head or the foot of the bed is strictly forbidden, regardless of the position of the bed.
Hydraulic or electric rotating facial beds or treatment tables are not designed for massage. Excess downward pressure can cause instability.
Aligning the bed perpendicular to the base or using the bed on a slippery surface may cause the bed to become unstable. Injury to patron may occur.