Call me paranoid, but if I wrote the e-mail draft at an eerie hour, I'd save it and click the "Send" button during business hours. I've been to writing conferences where I hear people are judged on their appearance--are their clothes nice? Do they shower? Do they take care of their teeth? All these things are meaningless and superficial, but supposedly give a sense of professionalism and stability.
I dress professionally at conventions and send e-mails during daylight hours to promote that sense of reliability/stability. I want to be clean-cut and rock-steady while I'm on the agent hunt. I can let my hair down and stop covering my natural weirdness once I've been published a few times.
IME, agents understand and expect that writers have day jobs and lives, and almost expect communications at odd hours. FWIW, I've not only sent emails to agents at all hours, I've received some frome agents at all hours. Hell, many agents and editors pop up on my twitter feed at all hours.
While I agree with you about the professional appearance re clothing/personal care, and I would agree that your emails themselves should be appropriately professional, the timing is, IMO, irrelevant.
And, FWIW, my interactions with agents at conferences have also run the gammut from business attire at more professional and national conferences, to appropriately comfy wear at writing retreats. it's all about knowing the environment and expectations.
On emails, content and appearance of the emails needs to be professional, but I agree with another poster that I'd be more concerned with sending a writing-related email during my day-job hours reflecting badly on my professionalism more than sending one at 3 am.
~suki
