Yeah you go to the first major town (Jubilife or something) and visit the GTS building on the west side of town. You enter, ask to go in, save, add then connect to Nintendo's service. Don't worry about sorting your party first before going in... you can access everything in the GTS, even your boxed ones. Do worry about items though as they get sent with the pokemon if you trade or offer it and you can't remove items in the GTS.
From inside you have 2 options. Search and offer, and both work in similar ways. For example, to search you first pick which pokemon to search for based on the first letter of their name. Now a catch here is that the only pokemon you can request is any one that you have *seen*. You can also specify gender and level if you'd like. After all that, you tell it to try and find some matches and a few characters are displayed below. You can then use the stylus to click one and see what they want, and then B to back out (HATE that interface).
I run into a lot of crazy requests though, and as such have never had success searching. What I do is instead make an offer. For instance I put up a Biddoff, lv9 and asked for a Male, lvl9 or less, Pikachu. You can only have one outstanding request at any point in time, but you can continue to use the search feature after you put in your offer.
After that (and to finally get to your question!) you can leave the GTS, save, and then shut the power. Later on you can revisit the GTS and if someone accepted, then the first thing that happens after you connect to the wifi is you see the trade animation with your new pokemon. I've made 2 trades this way, waiting 12hrs and 24hrs. (It may have happened sooner, but that's just how long I went before checking again)
So yes it's exactly a drop it off and check it later system. The pokemon is unavailable for use when it's up for trade. This is also why I think Nintendo can fulfill some trades for common types with canned names and generated pokemon.