No. Almost no pest known will simply go away on its own. The only reason for pests to leave is if shelter, food and water are removed and since that never happens you will require treatment. Leaving them untreated or waiting for them to go is a big mistake as they will spread and breed causing more damage and costing more to remove.
The only exception to this is that sometimes bees’ or wasps’ nests can be abandoned but again it is unwise to presume they will do so.