I have recently applied for a job online on totaljobs.com. I sent a copy to my email address, and I realised that the time was 2AM when I applied!
Do you think this will frowned upon by my (possible) future employer?
It's unlikely to negatively affect your chances, or even get noticed, for that matter.
The fact that someone stayed up a bit later than the norm on one given day would be an illogical factor to include when trying to determine whether said person will make a good employee or not, as it doesn't say a whole lot regarding that, and there are a lot more important things to consider in this regard.
However, it's anyone's guess how any given employer will see it. So, if it's all the same to you, do try to avoid it.
Employers are just people. I'm sure you will find someone somewhere in the world who will scorn your timing. And you will probably also find someone who will cherish it. And then you will find a vast majority who won't put thought into it.
The question is: Do you want to work for an employer who thinks less of applications submitted at night?
If you think it's unreasonable to sort applications based on e-mail timestamps, chances are this employer will have other unreasonable traits that could spawn conflict between you.
This employer would be doing you (and him) a service by rejecting your late night application.