I've heard and read Dutch Sheets tell this story. He was going and praying for a woman in a coma every week (he did this for a year and she finally came out of the coma. Deemed a miracle by the doctors). During this time there would be someone else in the room with her from time to time (I assume maybe it was a nursing home type setting).
He goes in one day and there's another woman in there in a coma also. He noted there was always a radio between the beds playing soft secular music every time he went. So he's praying for the woman he normally prayed for, and the Lord spoke to him about the other woman in a coma and told him something like 'I want you to lead her in salvation'. Well obviously she's in a coma and he's wondering how do I do that? So he goes over to her and basically talks to her about Jesus and prays for her for salvation, and says a 'sinner's prayer' like we are talking about in this thread, and prays it as if she could repeat it after him. He said the exact moment he said 'amen', on the radio (that only ever played secular music) Amazing Grace started playing on bagpipes. Do I believe God saved that woman? Yes. She couldn't speak, but God will meet every person where they are physically. He's certainly not going to deny anyone salvation just because they aren't capable of actually physically speaking.