You would be crazy
Remember, gutters get clogged and then you may have to do more than just unclog your gutters if you do as you described. Makes me shudder to think of it.
You could use 20mm round pvc conduit under the rainwater gutters or assuming the soffits are white you could fix it along the soffits. I use it outdoors and use PVC weld adhesive to seal against weather (not designed to be used outdoors) using the PVC weld adhesive that is meant for PVC waste pipe works well to seal against weather. I wait until everything is fitted then and only then do I use the weld adhesive. It's far cheaper than using direct burial cable and almost as effective.
The best thing is if you ever do need to replace a cable, fishing cable through this stuff is easy.