No, generally not. The total amount paid for the vacant land would be the amount paid as well as any fees at closing like attorney's fees, recording fees, surveys and similar costs. If they had to do any demolition to an existing structure, the costs would be added to the basis.
This IRS publication has a list of costs that can be added to the basis of the property. Interest and property taxes can generally be taken as an investment deduction in the year they are incurred. If your parents did not take this deduction and specifically elected to add the costs to the basis of their property, then they could be added to the basis of the property. They are considered "carrying costs" to hold the property and you can read more about adding them to the basis here. If they did not make this election every year that they did not deduct the interest and taxes, then you cannot add them to the basis of the property.
