I notice it more Online (for some reason) than I do offline, but yes I also find it very dark under heavy clouds during the day (obviously). It never got that dark on my monitor but that was before DX11 so can't really compare, but on the S397 servers I have had to put the headlights on and I never had too before.
As with everything you need to compare to Real Life and yes it can get dark enough for headlights in the day, but for me there is something amiss here as it appears too dark (Standard Cloudy weather as is on the Server so it's not a Heavy Storm which would require headlights for example), like a Contrast issue perhaps, as it gets overly dark for my personal liking.