Yes. Essentially, what happens when a donor chooses to cover the cost of the donation is that their donation is increased to offset the amount of the fee. Later, the fee is deducted and the entire intended donation amount is given to the church. So, the entire donation (including the fee if the donor chose to cover it) is tax-deductible.
Note for accounting: A recommended way to account for fees is to credit each donor with their full donation, and then debit the fee amount as "service charge" or a similar category.