No.  Health Savings Accounts (HSAs) can be set up at any time and do not need to be set up to accompany an HDHP.  High deductible health plans operate just fine by themselves; a Health Savings Account is a compliment to an HDHP but is not required.

An example of a scenario where someone would not need to set up an HSA is if they weren’t contributing to it due to extremely low medical needs.  There would be no sense in establishing an account just to have it have an ongoing balance of $0.00.