I've done this a few times now and there are some caveats (some obviously intentional and some not-so-intentional). I found that if I retire the fortress and start with an adventurer from the fortress, I am not allowed to sleep there for some reason. It's not a huge problem, but it means you can't use your old fortress as a base to work out of. If there are no close by towns, you will need to get travelling companions so that you don't meet an untimely end by the boogey men.
You can solicit companions from your fortress as normal, although the times I've played I haven't had a high social standing so everyone said "no". I *think* that the easiest way to recruit companions from your actual fortress is to make sure that they are doing militia duty (patrolling, training, whatever) when you retire. This will turn them into mace dwarfs, etc, instead of growers.
While you are adventuring, your fortress will get many, many visitors. When you unretire, these visitors will still be there. You might also even get new citizens while you are away (I even got a goblin citizen once!). If the caravan comes while you are away, there is a chance that the merchants will become part of your fortress. They are a bit like performers in that they do nothing other than hang around in your locations. Presumably they can petition for full residency after 2 years, but I haven't tested that theory. Sometimes visitors will be "hostile". They will mostly do nothing but stand around. If you get attacked, they will come to your aid and not attack you. The only time they will attack you is if you attack them or if there is a loyalty cascade (in which case some of them will attack you). Eventually they seem to leave the map (just like normal visitors). It's a bit creepy (especially if they are standing around in your bedrooms), but they don't seem to be harmful.
When you unretire a fortress, all of your citizens, pets and livestock will be randomly distributed on the map. This is potentially bad news if you have dangerous creatures locked up somewhere. I believe (but haven't tested) that creatures in cages will no longer be in cages. Almost everything in containers will be removed from the containers. So if you have lots of stuff in bins, then they will be taken out of the bins. The worst aspect of this is that all of your booze will be on the floor. So before your retire your fortress, make sure you have a reasonable stock of plants so that your can restock your booze. Also make sure that you have access to water in the mean time.
I found that it took me about 2 months to clean up the mess when I unretired a fortress. It's not really a bad problem. One other bad downside is that your manager work orders will all be cleared. I run virtually automated forts, so this is a pain, but it's also fun to make the orders so I don't mind so much ;-)
As for running in adventure mode... It's kind of fun to run an adventurer from the fortress (you will get a new dwarf, so basically it means a "special" immigrant). The main reason it's fun is that they know all the people in the fortress and you can tell stories about them to learn their back stories (without having to go into legends mode). I have not had a vampire yet, so I don't know if it will betray their secret or not. Travelling around is quite fun and you can learn about the history of your surroundings by telling stories.
The other nice thing about doing this is that you can explore and learn about the musical and poetic forms of your culture. In fortress mode, it's pretty much impossible to understand what's going on. But in adventure mode, you can browse through the songs you know and it will tell you which instruments it needs, etc. This is really useful for knowing which instruments you need in your taverns and temples.
I'm currently trying to play through a kind of "campaign" where I started with an adventurer in year 5 (so that there is not much history, art or locations to overwhelm my feeble brain). I played him for a month or so and then he sustained an injury where he couldn't use his right arm. I then retired him and built a fortress right next door with the idea of building a hospital. Once the hospital is built, I'm going to move my adventurer in it. Eventually he will probably get restless and upon hearing a rumour that becoming a were-beast will cure his arm he may set out in search of one.... Well... that kind of thing anyway. I'm also curious to see if strategic placement of fortresses coupled with incursions into opposition locations can eventually allow my civilization to conquer the world.