Yes, although the budget will show billing rates based on the default role billing rates, you can change these per project.
When building your Project Budget with Roles as your Budget Method, the default role rates will show as the Project Rates automatically on the first tab. To make changes, click on Project Rates:
As project role rates can vary by project, a person can be assigned to the same role but have a different billing rates on the project.
If you are looking to have the role have different billing rates based on who takes the assignment, this can only be accomplished by creating individual roles for each person.
For example - "Engineer- Sam Smith"
You can then set the individual billing rate per person and adjust them for each project as needed.
Please remember to ensure that the person's contract details have them assigned to the correct default role:
Did you know? You can bulk edit hourly rates in Manage > People > Bulk Edit. Or you can also use the CSV tool in Settings - People.