Random and probably silly interview question

I will be graduating in December, and there are people from the class before me who graduated in May and are still looking for work. I have been applying (and collecting rejection letters) for a month already. I'm a slightly older student at 35. My maybe dumb question is should I color my hair. I stopped coloring when I started getting REALLY grey. Right now I'd say I am 40% grey and it is coming in as a pleasant salt and pepper look. I hated spending $80 or so dollars I didn't really have every 6 weeks and it was starting to be extremely noticable between colorings. I've tried the DIY store bought boxes but they wash out in 2 weeks or so from my hard to color hair. So anyway I look a bit older. I've had patients remark they thought I was in my 20s when my hair was up but with it down there is no fooling anyone.

With the job market this bad, would it matter at all if I colored my hair? Will anyone care? I like it natural but NEED a job like I need to breath oxygen at this point. I've seem a few hints that it's harder for "older" grads. Am I overanalyzing as usual?