not necessarily. you can always pay the minimum amount for a high priority transaction but mark it as RBF and if it didn't get confirmed in the next block and if you made sure that the mempool had indeed grown (eg. you can do it on https://jochen-hoenicke.de/queue/#0,24h) then you can simply bump its fee before the next block is found to the new minimum for high priority.

keep in mind that each time you bump your fee your transaction ID changes and although majority of services that i have seen have no issue with RBF and those that had bugs have fixed it already you may want to know what kind of service you are using in case your payment is to such services for a purchase for instance, otherwise deposits in your accounts like on an exchange have no issue.