I'd definitely wonder if somebody was OK if their appearance changed dramatically from how they'd always been, particularly if they had always been somebody who did hair and makeup, nails, etc, religiously.
I'd word it differently to the 'let yourself go', though, I'd say something like 'I've seen your appearance change quite a bit/I'm used to you wearing makeup and it made me wonder if there's any reason for that change'.
The easiest way to know for certain that a teenage girl is very unhappy about something is for them to turn up without a scrap of makeup and their hair isn't done when they've been doing it for the last two years without fail.
For colleagues, it's two things - either not doing hair/makeup at all, or, where they don't normally do it, they've suddenly turned up with it done (and it's not staff photo day or a special event). The latter gives a feeling that they're either trying to put a brave face on or they feel terrible and are trying to hide it. Sadly, the latter can also mean they're trying to cover up bruising sometimes.
Men aren't that much different - if one stops shaving so regularly, their hair grows longer or their nails look untrimmed, it's often because there is something wrong. I know several who put on weight when they're unhappy because they don't eat as healthily, stop exercising or have started drinking more. And it's often clear when they're feeling better because they will 'smarten up' again.
So it's normal to notice and consider if there is a problem when somebody's appearance changes.
But to put pressure on to look 'better' is wrong.