Perhaps you could use a copyrighted image as a trademark without permission, but you wouldn't want to actually do it. The problems are severe enough that I don't think there would be much actual precedent (because few people would make a good faith attempt to do this sort of thing without violating copyright or trademark laws), but we can still look at the text of the relevant laws.
According to 17 USC 109(a):
Notwithstanding the provisions of section 106(3), the owner of a particular copy or phonorecord lawfully made under this title, or any person authorized by such owner, is entitled, without the authority of the copyright owner, to sell or otherwise dispose of the possession of that copy or phonorecord.
And according to 17 USC 109(c):
Notwithstanding the provisions of section 106(5), the owner of a particular copy lawfully made under this title, or any person authorized by such owner, is entitled, without the authority of the copyright owner, to display that copy publicly, either directly or by the projection of no more than one image at a time, to viewers present at the place where the copy is located.
So let's say there's an image you want to use, and it's published in a magazine. You can't legally reproduce that image. But you can buy a thousand copies of the magazine and a pair of scissors. You now own a thousand lawfully made copies, and can legally display or sell them.
But as I said, there are severe problems. Your logo will literally just be glued on; you have to use the physical page from the magazine and can't simply print the logo on your packaging or product. You can't use a blown-up or shrunk-down version; you're stuck with whatever size you could find. You can't really modify the copies, as that would mean you'd be creating a derivative work (unless you modify them so much that it becomes a parody or otherwise transformative, in which case it could be fair use.) You can't put the logo on TV, or in newspapers, or on the Internet. It's fairly expensive to buy a magazine for each product you want to sell. And once you run out of copies, you can't make more.
You also could run into trademark-related problems. Depending on the circumstances, the author could argue that you're misleading people into thinking he is associated with your company or product. According to 15 USC 1052(a), if a proposed trademark contains
matter which may disparage or falsely suggest a connection with persons, living or dead, institutions, beliefs, or national symbols, or bring them into contempt, or disrepute;
then the registration can be refused.