Suckers produce more flowers, which lead to more tomatoes, and more seeds, to plant. If all suckers are removed it could lessen the yield. Each sucker you let grow can be a chance for an additional fruit set. Sometimes during the season the majority of the flower clusters on the main stem will open when the temperature or humidity is not right for pollination, which can result in blossom drop. If you have pruned all the suckers, the plant will bear little fruit, leaving no way for the plant to produce additional flowers after the hot weather has passed. If you kept the suckers, the number of flowers would be greater, and those flowers more than likely would open under ideal conditions, in turn increasing the yield of the plant.
Suckers left to grow also flourish with additional foliage cover. When it gets really hot and the heat is beating down on the plant this will help with sunscald. The fruit is shielded with the shade of the leaves.
Managing suckers depends on the type of tomato, too. Determinate tomato varieties grow to a specific height and width, then produce flowers. In a way they are self-pruning, and removing suckers could reduce the yield of the plant. But it does extend the main growing stem quite a bit and will generate suckers at each point of a leaf stem attachment. Indeterminate plants can grow out of control as suckers produce more suckers and then the plant is a tangled mess at the end of the season.
One method is to top the fruiting branches and stems at a certain height of controlling the growth. Because more flowers will pollinate and ripen before the end of the season, topping will also ensure that a plant does not put energy into tomatoes that are growing that will never be able to ripen. Removing the top of the plant is a great way to prevent the plants from becoming top heavy, so when winds, and heavy rains come, they could topple or branches get bent. Topping is simply pinching or cutting off the main stem or growing tip at the top of the plant. Do this on a sunny day, and while the plant does not have a large stem.
Early in the season you can root suckers. Suckers can root very easily in early summer, around here, early July. To do this, cut around 6 inches of sucker off the main plant and place in a glass of water. After a good set of roots form, put it in a pot with some new potting soil. Keep it watered in a dappled shaded area for a couple of weeks, then put it in the garden. New growth should appear in a few weeks, and you will have another tomato plant. Do not water too much or the plant will dampen off. Let it get totally dry in between watering.
Experimenting in your own garden is the only way you can test results. Every gardener has different soil and conditions. Do what works best for you, then if it works, go with it!