Consider this more as a longer comment but as an answer:
Let my try to analyze the differences between weights and resistance bands from a "physical" point of view in two steps: free weights vs Cables and Cables vs Resistance bands:
Free weights vs Cables
The main difference in force production is that gravitation always points down to the earth, whereas the force produced by the cables always points into the direction of the cable.
Consider for example a standing biceps curl. Using a weight the force you have to overcome always points to the ground.
If you use a cable to do this, the angle of the cable to an vertical axis changes during the motion and such the direction of the force you have to overcome changes. This depends also on where the cable is attached to the next deflection roller.
Note that in this and almost every other exercise you have to keep in mind that the lever arm changes during the motion and such the produced torque, which seems to be more relevant when thinking about what has the muscle to work.
Then one might try to capture so called strength curves (one axis: torque, other axis angle) which gives experts some information about how good a exercise stimulates a muscle.
Another difference between free weights and cables is that with free weight you can perform explosive movements where you also have to use forces to overcome the intertia of the free weight.
Free weights and resistance bands have in common that they produce a constant force along the line of action.
Cables vs. Resistance bands
Additionally to the differences discussed above resistance bands do not produce a constant force, but the force increases when the band is stretched. Not that this relationship is not even linear.
The key factor here is the relative and not the absolute elongation. I.e. if a resistance band is stretched by x percent of the original length it produces a particular force F(x) which does not depend on the original length.
So using a resistance band the force increases during the range of motion of the exercise. However using resistance bands you can get similar strength curves as with free weights so in some cases the muscle stimulation seems to be comparable to free weights.
Other comments and Conclusion
When training with resistance bands you should keep in mind the same points as when training with weights:
- get a proper nutrition such that your body has the building blocks to repair and build new muscle (protein, carbs, etc).
- get a proper recovery time
- have a large enough training volume per muscle group
- choose the right amount of resistance such that you can just do 8-12 reps per set
- increase the resistance in small steps over the time to keep the rep range above
For the last point it is important to have a resistance band set wich allows you to change and combine bands easily, such as the systems by bodylastics, lifeline-usa or gorilla-strength-gear.
For certain exercises you want to decreas the effect of increasing resistance with elongation in resistance bands. For this instead of taking the band shorter you should take the band as long as possible (or even two bands in series) and choose a heavier band instead or even better use several lighter bands in parallel to get the right resistance for you. This is because the increase in resistance depends on the relative and not on the absolute elongation as stated above.
For example when doing squats, you can do squats with the bands at your sides, armes hanging down. Then you have a strong increase of resistance force on the way up. Contrary doing overhead squats will give you a more constant resistance because the relative elongation is smaller (though the absolute elongation will be the same).
This can also be done by a sheave construction such as in the follwing patent: https://docs.google.com/viewer?url=patentimages.storage.googleapis.com/pdfs/US20130035220.pdf
Another important factor in using resistance bands is where to anchor the band to get the correct strength curve for optimal muscle stimulation. See this paper: http://www.ncbi.nlm.nih.gov/pubmed/21757393 and this blog article for a summary: http://www.hygenicblog.com/2013/03/20/quantifying-torque-in-elastic-resistance-exercises-part-i/
You can even think about using some sheaves to get a proper line of action of force for your exercise.
I think it should be able to build mass with resistance bands alone perhaps complemented with body-weight exercises. However it seems to be more complicated since you have to control more variables and there is not much literature about it with form pointers and guides to follow.
I am planning to buy a bodylastics set and try if it is possible to gain mass just with this and bodyweight exercises.
Since I also have a strong interest in this question and since this topic is not good documented in the web I give a bounty to this question to get a more in sophisticaded and more in depth answer.
I will add further references and diagrams later.