Does swishing your saliva around your mouth help prevent cavities?

No. The best prevention will always be proper brushing and flossing.
Sort of. Saliva is very good for your oral health because it rinses debris off of your teeth. Swishing saliva may help prevent cavities in conjunction with other good oral health practices.
Protection. Your saliva is your mouth's natural protection. Anything you can do to increase salivary flow can have a beneficial effect. However, brushing and flossing are more effective as plaque can be very sticky.