Crikey ladies...handbags away! Saying something along the lines of "I've done ICE installs before so I must be right" then being wrong is a good way to make yourself look like a chump! All these things are a constant learning process, so it's best to approach them with caution, especially where the facts are a little blurry. I've also done several ICE installs (and as it happens when I'm not being a student I earn a pittance as a live audio and lighting technician/engineer), but I'm constantly learning new things about the subject area. Anyway...
Firstly, leaving an automotive coil active without load for a long period of time will damage it - full stop. Whether or not it will *in this application* is another matter. As far as I'm aware (mine certainly doesn't), 300s don't have a 'stage one' key position - it's off, ignition/run, starter. Some modern cars have relays which disconnect it after a set time, so 'burning out your coil' has slipped from the forefront of the public mind - I was forever warning guys who'd have sound-offs at school about this. I have no idea whether or not the 300s have this feature.
As for flattening the battery...let's be scientific about this. A given battery has an Ah (amp hour) rating. A 100Ah battery in good condition can draw 100A for an hour before it goes flat. Let's say the average fairly modest (say '300w' - read: 150wrms - read: probably about 80w at 50% duty-cycle and full bandwidth...cough cough) 'sub and amp' setup will draw about 25A peak draw, you can run it for four hours *at peak draw* before it flattens the 100Ah battery. Also bear in mind that audio is a dynamic signal, and it has very little power in anything other than the lowest octaves - you'll only pull serious current with bass-heavy music. On top of that your *average* current draw will often not make it out of single figures, even with a '30A' system. (Note: I've not checked what a reasonable Ah rating is - that's just a figure off the top of my head.)
My quick answer to your question...
No, you needn't worry about flattening your battery in less than 30 mins unless you have a really powerful setup - tell me you've got a 1200W competition quality power amp and I'll think again.
Special - I may have misread you, but *normally* the bulk of the current for a HU is drawn from the 'constant' feed, with the ignition feed being used more or less simply as a 'trigger' - like the remote line to a power amp. Of course your HU may be different - but that is the 'standard'.
Anyway, lets calm down the ranting, all take a deep breath before replying, and not doubt each others experience, as we can all be wrong - and must be ready to accept when we are! Even Hugh...

Arf arf arf...
cheers
James