Yes, the salaried exempt employee may be docked for whole days of time off for which there is no vacation pay available.

Salaried exempt employees may not be docked for partial days.

This can be found in the FLSA (Fair Labor Standards Act) at the DOL website:The U.S. Department of Labor Home Page

Most employers have little difficulty determining whether a worker qualifies as an "exempt" employee under the Fair Labor Standards Act ("FLSA"). Generally, if an employee is paid on a salary basis and meets the job criteria of an administrative, executive, or professional employee (the so-called "white collar" professions), the employee is exempt from the overtime provisions of the FLSA. Seems simple enough. However, many employers unintentionally jeopardize this exemption by instituting pay and disciplinary policies that treat these employees as if they are nonexempt. In particular, policies that dock exempt employees for disciplinary reasons or require the use of paid partial-day absences raise questions about whether the employee is really being paid on a "salary basis" as required by the FLSAs regulations. The consequences of these policies can be substantial and include potential liability for overtime to the affected employees.
The DOL regulations recognize several instances where an employer may make deductions, or "dock" employees, for absences of a full day or more without jeopardizing the exemption. An employer may make deductions when the exempt employee is absent from work for a day or more for personal reasons, such as when an employee takes an unpaid personal day. Deductions also may be made for absences of a day or more because of illness or injury if the employer has a bona fide plan, policy, or practice that provides compensation for loss of salary due to sickness or disability, such as a policy that allows employees to accrue paid sick leave. This deduction may be made even if the exempt employee has not yet qualified for the plan or has exhausted the plans sick leave allowance. However, if a private employer makes deductions from an exempt employees pay for absences of less than a day, the employer is considered to be treating the employee as an hourly employee and may jeopardize the exempt status.

Shirley