I don't think this is true, or at least not true in all cases.
From what I've seen and talked about with friends who have poor time management skills, a big problem is they get distracted and don't stay on task. Thinking about the clock doesn't really enter into it in that case.
I'm a little confused what you mean by time management skills, now, too. Can you give an example of a scene that required them, and how it would look for someone with good skills and how it would look for someone with bad skills?
Like, I have a friend coming over around noon today. I need to shower and get dressed before they get here. That takes like half an hour. I might just set an alarm on my phone for like 11:15 so I remember. I'd set it to 11:15 to give myself some extra padding. I know I shouldn't do anything that might take longer than the time available, like go for a long bike ride or start playing a video game that can't be paused.