Generally, yes. While an organization's exemption application is waiting for approval from the IRS, the organization may operate as a tax-exempt organization. If an annual exempt organization return is due, the organization must file it, indicating that its application is pending.
Although donors have no assurance that contributions are tax-deductible for federal income tax purposes until the application is approved, contributions made while an application is pending would qualify if the application is approved. However, if the application is disallowed, contributions would not qualify.