Okay, I went off on a huge tangent. Short answer is yes, you can easily keep and breed shrimp in a vase. Cherry shrimp are preferred unless the vase is in a room that is temperature controlled to a range that supporst more sensitive species (unless you build a chiller).
Now on to the excessively long response I wrote on my iPhone, which took way to long to write to just delete:
I know this thread is initially almost a year old and the OP has probably either set this up or moved on with another idea, but I'll add my experience. I have done several planted vases that were all successful. Heck, I've even got a reef tank that has been running almost a year that is built in a 6" square vase (was a planted vase at one point). Granted, the vase is now drilled with an overflow and return lines and has a sump that bumps the volume up from 1/2 gallon to 1 gallon, but it ran successfully for a couple of months with no filtration, just cleaning everything off daily with a dropper.
I have done capped soil, just sand, and just Black Diamond. All three methods worked successfully. Tanks set up for 1-2.5 years. They usually had small fish that barely exceed 1/2" when fully grown. No more than three fish (Endlers or Heterandria Formosa) since the vases were a half gallon or so, and neocardinia (cherry, sunkist, or fire red). I did try a few CRS at one point, but they couldn't take the summer heat (187 year old house with no central cooling or A/C). The shrimp bred (other than the CRS) as did the fish, which necessitaed moving the adults and setting up another tank. Plants were all fairly low demand that were not prolific growers, I learned my lesson early on with water sprite.
If the tanks were inert soil, very careful dosing was managed (usually complete macro and trace like Flourish, no carbon source like excel though. Too easy to stress the animals and I found it wasn't necessary as there was sufficient gas exchange with the shallow volume) by mixing into a larger volume like a 1 gallon water jug and saving the remaining water for other vases if I had multiple ones running or for future water changes if only one was going. I went super weak on the dosing, mostly just enough to keep the plants healthy but not growing vigorously to prevent the vase from being overgrown every other day.
Water changes were usually 50-75% every week or two depending on how things were going. Surface film was cleared by placing a section of paper towel on the surface. There was never surface film when I had water sprite, but it usually grew too fast and completely filled the tank in a week or two. A section of rigid airline in the end of standard flexible aquarium airline was used as a siphon.
I never used lighting over the vase. They were either in a room with lots of large windows (shades typically drawn so no direct light, just a lot of filtered light) or in close vicinity to larger tanks (relatively speaking. 2.3-7.5 gallon), which provided sufficient light for moderate to slow growth. The depth on vases is usually fairly shallow and the dimensions are such that light penetration is not an issue unless prolific plants are selected. Even then, small lamps are sufficient.
Algae was never an issue as nutrients were kept low and were mostly supplied by feeding. A single nerite did a sufficient job at keeping the lite dusting off the glass, although they do wander occasionally and need to be placed back in the vase.
This is just how things worked for me. You can set one up pretty much how ever you want and can go for fast growth high demand plants, but that will require trimming every couple of days, which can be time consuming, but will also help to keep you involved with everything and playing with the tanks on an almost daily basis, which is great if you have the time.
Have fun and experiment, there are no set rules, just be cautious and aware of the life you put in there.