Making my first batch! Using a Brooklyn Brew Shop kit, and did the active part last night. I've got the jug in a cool/dark place and it it bubbling away, sending CO2 through the tube in the top of the jug into pot of bleachy water. My question: why bother taking out the tube and installing the airlock, like the instructions say to do after a couple of days? Why not just leave the tube in there, going out to the bleachy water? Seems to serve fine, but then there might be something I haven't considered.
Short answer: sure, that is fine and jsled is absolutely right.
Long answer: the other thing to consider is just don't bother with blowoff, which I assume is the reason for the bleach water setup, and just use an airlock.
I think being really concerned with blowoff is probably a side-effect of following old Charlie Papazian instructions or people who followed his lead. I know he said blowoff gets rid of a lot of unwanted gunk and fusel alcohols that affect taste of the finished product, but I'm not so sure that's true in a negative (or any?) way and I don't think large breweries tend to worry much about blow-off either. Plus it seems to me there is a slight risk of infection from using/changing blowoff tubes.
You need blowoff if your vessel is too small, but nowadays I personally would use a bigger vessel.
Using an airlock certainly makes handling the vessel easier as it's all self contained, but hopefully you won't have to handle the vessel much.
I liked using an airlock because it was a more compact and simple setup. However, after having a batch overflow the airlock and make a mess while I was out of town my wife insists that I use a blow-off. I'm happy to do that as there is little functional difference between the two and using the blow-off tube eliminates the chance of making a mess again.