SPRINKLER TALK FORUM - You Got Questions, We've Got Answers

So here is my genius idea (or brain fart, depending on its feasibility). Here at the conference center we have a newly placed 'garden' in our recreation area with some trees bushes and flowers. Watering it is sort of an issue, since there is water available but it has little to no pressure. Its at the top of our water supply basically, and that is what I blame for the pressure (or lack thereof).
The 'garden' is next to a large pavilion which is already fitted with gutters and downspouts. I want to harness these downspouts into rain barrels and then try to run a drip line off of those rain barrels.
What do yall think it would take to make this work? Feasible? Do I need a pump or will gravity do anything? THANKS!