User wants to enter generic expenses to a project that aren't linked to any employee. Is it possible to create expense entries without having to tie them to employees?

Unfortunately, the Expense Entries screen doesn't allow you to enter an expense entry without it being linked to an employee or vendor by design. You can pick any employee for this purpose as a workaround. Commonly, the Office Manager is chosen for this. If this does not work for you, you can create a generic employee profile solely for entering general project expenses.