There is no requirement to allow additional deposit to a CD. If you choose to allow additional deposits, you can limit or condition them however you want, as long as you disclose it properly.
An HSA account can be a DDA, Savings, or a CD in any combination, if you have the ability to service such an account. It is no different than an IRA, which can have a cash account and also be invested in a wide variety of investment vehicles, i.e., CDs, stocks, bonds, etc. The HSA account is the over riding parent account, the investments that are held in the account are more like sub-accounts.