Fortress mode and adventure mode are very nearly two completely different games in the same wrapper. The only real overlap comes from the fact that you can have adventurers migrate to your fortress, assuming they're dwarves (and bringing with them all those excellent combat skills you trained them in), and the fact that you can visit your fortress as an adventurer (allowing you to craft fantastic adamantine weapons, store them in lead bins so they don't scatter far, and then find and use them as an adventurer).
At least, that's the only real overlap currently.
Plans exist for allowing adventurers to start settlements with their companions, effectively building their own communities in the wilderness. How this will work has not yet been determined, as far as I know, and it will operate on Adventure Mode time scale, which (if I recall correctly) is 72x slower than Fortress Mode.
A lot of the attention looks like it's focused on adventure mode for the time being because adventure mode allows you to go out and explore the world in a way that fortress mode simply doesn't as of yet. When the time comes that you can order your armies out into the world, a lot of the features that are only visible in adventure mode may become much more visible in fortress mode. Even before that point, there's a chance that we'll see enemies that can climb walls or jump across gaps in fortress mode - features that, last I heard, are currently only present in adventure mode.
The same goes the other way, too. Currently, only fortress dwarves can pick wild plants. In the next version, adventurers will be able to pluck fruit from trees, and Toady has said that he wants to make a similar feature possible in fortress mode. I seem to remember (but unfortunately, don't have a quote handy) that he also said Adventurers will gain the ability to pick from shrubs, too. It's a small thing, and it can make a huge difference to adventurer survivability if you simply can't find anything to kill for food.
Because the mechanics of each mode differ so greatly, I don't think that one truly prepares you for the other in a control sense, though as I outlined above, it's possible to play a fortress to create gear that can then be taken for use by your adventurer. By the same token, adventurers can go out and scour the world looking for cool items, then leave them in a lair somewhere for you to embark on. Nothing says easy start like six picks, six battle axes, a small heap of whips, various pieces of armor, and a pile of bones waiting to be made into your first bunch of crafts, all of which cost you zero points on embark and which aren't scattered all over the map from a previous abandon. In theory, a diligent adventurer can gather for you enough items to completely outfit your first couple squads of dwarves.
Oh, one thing of note: Next version brings the ability to retire a fortress without abandoning it, create a dwarven adventurer, and travel the world before having them retire in your fortress, where they will be a resident when you switch back to fortress mode. With a little time spent, you'll be able to have a ten dwarf squad of demigods, all pre-trained in the art of combat and delivered right to your doorstep.