I guess the first question to ask is why won't you have access to barbells? You can tweak SS to use dumbbells only, but I imagine the results won't be quite as good. It's certainly still better than doing nothing, and if you're a beginner, you'll still make some good gains, but the barbell alternative is still the preferred choice. Some issues I can see you having:
* I'm not sure the dumbbell version of the squat is quite as effective as the barbell version. I've never done it myself, so I could certainly be wrong, but I get the impression that holding the weights in your hands at your sides, instead of on your back, really reduces the involvement of your posterior chain, hips, hamstrings, etc. Can you even get comfortably below parallel? SS is based on squats and their ability to involve a HUGE percentage of the muscles in your body, so if dumbbells reduce it to just a quad centric workout, you're missing about 50% of what makes SS so effective.
* A dumbbell deadlift would end up pretty similar to a dumbbell squat, unless you do more of a Romanian deadlift.
* Finding heavy enough weights could be an issue as not many places have dumbbells over 100lbs. If you are a beginner, you'll do alright with less weight for most of the exercises, but even relative novices get to squatting and especially deadlifting that kind of weight pretty quickly.
* Grip may be a limiting factor, depending on the dumbbells. Holding a crappy, thin handled 100lbs dumbbell in each hand is much harder than holding a 200lbs barbell.
* Some of the barbell exercises start from a rack, but that's not really an option with dumbbells, so you'll need to work to get them into position. This will be an issue primarily with dumbbell bench press and especially dumbbell overhead press. Not a big deal initially, but as the weight goes up, it'll get tougher and tougher.
* Dumbbell exercises often make it harder to get used to the exercise for a beginner. Barbell exercises are hard enough to learn as it is. Having to additionally balance your arms separately may slow your initial gains. In some ways, this may make the training even more effective or functional, but starting out with barbells is typically a lot easier.