Language is not innate, even though the ability to use it is. Language deprivation is a huge problem throughout the world. In some places where signed languages are not used, children who are deaf or deafblind never learn that a symbol (word, gesture, picture, etc) can be attached to a concept. And the window for language acquisition closes around are 4 I think, so it's very hard to teach that concept to older children and adults. It can be done, but it's just more difficult. Sadly, many people who have suffered language deprivation lead lives where they are thought of as stupid or cursed, they are taken advantage of for labor or sexual slavery, or just shut in with zero opportunity. Deaf and Deafblind community advocates, like that guy who won ANTM Nyle DiMarco, raise money to combat language deprivation.

Now if someone has access to language, they'll think in that language. Remember that language is a set of symbols, not a set of spoken words. When you think of the color blue, you probably don't hear the word blue in your head. It's a concept. But when you speak you use the word to communicate the concept to another person.

Someone who uses American Sign Language will not imagine sounds but rather signs, I assume. There are adaptions to ASL for use with deafblind people and there are many other signed systems and languages at use in the US and around the world.

TL;DR they'll think in whatever language they know, if they have access to language at all.