In just a few minutes of Googling, every animal shelter link that I read seems to emphasize how important volunteer socializers are to the well-being of the animals in a shelter environment.

Here are some examples:

Anderson Animal Shelter: Dog Walking and Cat Socialization
Do you think dogs are divine? Do you fancy felines? If you like working one-on-one with companion animals, then our Dog Walking or Cat Socialization programs may be for you. The shelter can be a stressful environment for animals, and one of the best ways to ease their stress is to give them love, attention, and praise.
Dog walking volunteers work one-on-one with dogs and puppies, taking them outside for exercise and training, and giving them all the love they need to thrive in the unusual atmosphere. The Shelter can be a noisy and stressful place for dogs that have been lost or given up by their owners. Interaction with people is their best therapy. The Dog Walking Program gives the dogs this essential quality time with people who care about them. Weekday dog walking hours are 7 am - 6 pm and Saturday hours are 8 am - 4 pm. Sunday hours are 8 am - 4 pm. Dog walkers must be 16 years old or older.
Cat socialization volunteers perform a similar task, by holding, petting, and brushing the shelter’s hundreds of felines, allowing them to relax in the shelter and to understand that while there may be a number of strange smells and noises, Anderson Animal Shelter is a place that they can find love and attention. The Cat Socialization Program allows volunteers to interact with Kitty Country and Kitty City cats to help alleviate the animal's stress, thereby enabling the cat to become more friendly and calm when approached by a potential adopter. Weekday socialization hours are between 7 am and 6 pm. Saturday and Sunday hours are 8 am to 4 pm. Cat socializers must be 13 years old or older.
http://www.andersonanimalshelter.org/Volunteer.htm

From the UK – Save a Pet
Cat Socializing – cats need the love and attention of people even when they are in a rescue centre. Many centres have volunteers who will groom and give a cat attention. This is important as it keeps a cat used to the company of people and will ultimately help it settle quickly into a new family.
http://www.saveapet.co.uk/volunteering-pet-rescue-centres-animal-shelters.html

From the LA Animal Shelter Cat Room
This shelter has a Cat Brigade Committee as well as a Cat Socialization Committee.At any given time, some of the cats need extra socialization and some of the cats may be intimidating to people not used to more aggressive cats. Unfortunately, a lot of times the cats at the shelter appear to be aggressive when they are actually scared and not used to the environment.
http://www.boozhoundlabs.com/pups/catRoomBrochure.pdf

From Metro Atlanta
Kitty Buddy:Several cats at Good Mews require additional attention so they can become more adoptable. Active volunteers choose a cat or cats from the Kitty Buddy list they wish to work with. Kitty buddies are required to spend a minimum of 30 minutes a week with their buddy, helping the cat become more socialized. Only active volunteers are eligible to become Kitty Buddies.
http://www.goodmews.org/good/mews/info/volunteer_opportunities_committees/