Can "stark" be used as a synonym to "strong" or "of a strong will" in a sentence like "She was a strong person" or "You need to be strong to stay sane in captivity"?
I suppose you found something like the Merriam-Webster definition, which has it meaning "strong, robust". You may also note there that this is listed as an archaic sense of the word. That is to say, you will find it in old texts, or when people are trying to be deliberately anachronistic, but it is not used in that way now.
So no, you can't use it in that way if you want people to understand you.