No.

1. Look at how hard it is to move the syringe piston by hand, at 1 minute and 40 seconds.

Then
 consider if the weight of the sliding bolt / weights, on each arm could produce
that much force.  Answer is no.

2. This device is practically the same in principle as a dozen other methods that
also cannot and do not work.

3. The balloons appear to remain inflated throughout their immersion.

4. A balloon immersed to that depth cannot produce enough force to
move a hypodermic syringe against the friction it provides, even without
the additional force needed to lift the bolt / weights .

5. The video is cut and edited at 2 minutes and 30 seconds

6. The guy in the video is probably just trying to protect the invention
from being patented and controlled by big corporations and big governments,
by open sourcing it, just in case it really does work. 

         peace out
               floor

@ glaysonmestre

 go for it
It might be a fun project
  and
If you build one It might be worth it, just for the understanding
it could bring to you.

   best wishes
      floor