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, 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 habenHaben.