If it does it's because the converter had a defect. While I've never heard of such an issue the fact you asked means you had a bad experience or are just doing the Chicken Little.
The other complaint you get is folk that put 480i composite RCA into ANY converter usually complain about poor picture quality. You can't add quality. And these were usually on sets under 30 inches where 4K sets are 40 and more inches AMPLIFYING the display issues.
I have a VCR with RCA composite cables and a 4k HDTV. If I use a converter, will I fry or burn out my HDMI connection in my tv because it's a 4k tv? I believe the converter is good for 1080. I thank all who respond.