I do that a lot. As a faction leader, I like to make sure people get timely payouts for stuff, and that I'm aware of any major issues, so I do a quick login purely to check mail and logs. I often leave the tab open as well. If I'm not deployed, and I'm not in all chat, I am most likely not there. I wish DS did away/idle messages, but it doesn't.
I'm quite reachable. I check my in-game mail at least daily, and these forums an average of around twice per day. If someone leaves a message, I receive it, and I generally respond to it. Ditto on forum threads. There's no need to send multiple. I'll get it.
When people need to directly communicate, that's why instant message programs exist. It sucks that your parents don't allow you to use them, but there's nothing I can personally do about that, and I can't restructure my whole life around that restriction on yours. Trust me, I know what it's like to have pointless parental restrictions, and it blows, but other than "turn 18", there isn't a hell of a lot you can do about it.
I simply cannot afford to watch a chat (game or external) all day long. I'm 28, and my income almost completely died with the economy. I need to fix that ASAP, because my life is completely stuck in place until I do, and the longer it takes me to fix the situation, the worse it's going to get, and the harder it's going to be to move on in life. That's my primary goal atm. It has to be, and you need to understand that.