This is not possible. Customers and suppliers are actually subsidiary ledgers under Accounts receivable and Accounts payable, respectively. There is no such asset or liability control account under which other payers or payees could be created.
Besides, the work of setting a payee up under some kind of Other Payees list would be no different from what is involved in setting up a Supplier. The only difference is that your list would be broken into two separate lists, which would probably make things more difficult. There is no limit to how long your supplier list can be.
Other payers/payees are not currently covered by the auto-complete function, which is what you were referring to in your post. If they were, there would be no reason for a list. Your problem would be solved. This bug is the subject of another topic: Autocomplete for payer / payee missing.