The answer is... kinda. DE troops aren't going to be the backbone of your army at TH7, but they can still be useful anyhow.
You can earn dark elixir, either through clan wars or via raiding other bases. So if you train DE troops and use that to raid/win DE, technically that's a win.
Minions are by far the cheapest flying unit in the game, in terms of both resources and camp space. Combining them with the barbs and archers in the "BARCH" farming strategy makes the also popular BAM troop combo. The minions allow you to pierce deeper into bases your barbs & archers couldn't normally get into. This can help you hit DE drills and storages you wouldn't normally be able to otherwise.
Also it's worth noting that you can use overtraining to store your DE in your Dark Barracks when you're not playing. (the tip is about regular elixir, but DE works the same way) Just queue up DE troops when your camps are full and the elixir will be spent, but you can cancel them and get the DE back later.
This can help you save up or protect quantities of DE that you would otherwise lose to raiding. Whether or not you consider this "training DE troops" is kind of questionable, since you'll generally cancel the troops rather than train them.
In my personal experience at TH7, I used minions occasionally (usually I had around 10-15 trained at any given time) to hit DE storages during raids. I managed to earn my Barbarian King this way before ever having a drill.
Best Answer
The Dark Elixir storage is where Dark elixir is stored and is similar to Elixir and Gold storage buildings. Dark Elixir is used to train Dark Elixir Troops through the Dark Barracks, as well as buy and upgrade Heroes.
Dark Elixir Troops are extremely expensive to train (because of the rarity of Dark Elixir), but are also generally more powerful than normal troops. Dark Elixir troops reside in the Army Camp, similar to normal troops e.g. Barbarian, archer etc.
Heroes are super powerful troops that do a lot of damage. They are immortal, but if injured in battle must sleep to regenerate their health. There are two heroes, the Barbarian King and the Archer Queen.
You can acquire Dark Elixir from raiding, or with the Dark Elixir Drill which is first unlocked at town hall 7 and a second one at town hall 8.
As of the Dark Spell Factory Update (1/7/15), Dark Elixir can also be spent on Dark Spells which are simpler spells which although are more specialized, are more powerful (compared power-per-storage-space to their elixir counterparts) and take up less space.