I would say that it depends on a few things such as how long you are going to play, and your current physical condition. I am a physical therapist, and stretch and warm up for all athletic events I participate in. Pool, however, does not require the burst type of movements that should create acute trauma. That being said, it does require proloned positions and repetitive movements that can lead to chronic injuries, or aggravation of current injuries.
If I was in good health, and only planning on playing for 30-45 minutes or less, I really would not worry about warming up. If not in good health, or long bouts of play are expected, warm up may be a better idea. Anything that requires prolonged use and fatigue of muscles may benefit from proper warm up and stretch.
The low back and shoulders (particularly the bridge arm, although both can be included) receive the greatest amounts of stress during pool play. The bridge arm is put into a position that can "impinge" the rotator cuff between the upper arm bone called the humerus, and a bone from the shuolder blade called the acromion. If you already have shoulder problems, stretching your shoulder to allow better range of motion can help decrease this (although stretching alone may be the answer for an already existing shoulder problem). Also, prolonged play can put stress on this area that can lead to chronic injury. Therefore, it is an area I would consider warming up and sretching, especially if I was coming off of a shoulder surgery or injury.
The low back certainly takes a fair amount of stress with prolonged play due to the forward flexed posture of the pool stance, and the generally poor sitting posture people display while awaiting their next shot. The prolonged posture used in the pool stance requires prolonged contraction of the postural muscles of the spine, and can put abnormal pressure on the intervertebral disks of the lower back. If I had a history of disk injury, I would utilize some backward bending stretches before and periodically during play to help keep the disk's gel (nucleus ) in the correct position. Also, anyone with a history of low back strain or tightness will benefit from correct stretching of these muscles, as they will likely tighten some with prolonged play. It would not hurt the average Joe either if they anticipate a long session.
I would also consider warm up and stretch before play in those with chronic conditions such as carpel tunnel or tennis elbow. Any prolonged use of the muscle involved in these injuries will irritate them. Stretch and warm up will help decrease this.
I have not seen any real research regarding the need for warm up for pool play, but some of this falls under the common sense area given the nature of the game. This post is in no way an exhaustive view of stretching needs for pool, nor does it describe what stretches should be done for each thing. It was just a basic statement regarding the question. If you have more specific question regarding your own situation, feel free to PM me, and I may be able to be more specific that way.