False
There are mainly five interrogative pronouns: what, which, who, whom, and whose. And they are all used to ask questions. "That" has several functions but none of them include to act as interrogative pronoun. "That" can introduce a dependent or independent clause: "The gift that I want is in this store", it can help indicate a noun or pronoun in a sentence (A demonstrative adjective): "That is my guitar"; it can function as an adverb to show the degree of something: "I would not go that far", among other functions.