No, It is not added to the cost basis of the home.
Depending on what they used the reverse mortgage money for, the interest may or may not be at all deductible. This is still mortgage interest and still treated as such. That means, you can only claim the interest as an itemized expense in the year that you pay it. If you do not itemize your return you cannot claim the interest.
Additionally, in order to claim the interest on the mortgage, the money would have had to been used to buy, build or substantially improve the house. If it was NOT used to buy, build or substantially improve the house, the interest is not deductible.