As a general rule, the answer is yes. Since she is the biological daughter of a Cohen, her firstborn, if it's a male, is exempt from Pidyon Haben.

Being adopted has no bearing on her priestly pedigree.

However, as discussed [here][1], there are cases that would nullify the exemption. Specifically, if she had relations with a non-Jew prior to having her first child, then her firstborn would be required to have a Pidyon haben.


  [1]: https://judaism.stackexchange.com/a/19063/501