I don't know if that would be a problem for your slab but I would personally be concerned about it. A 1/4" rainfall on a roof generates a lot of water. You'd have to do the math for your house but I'm guessing it's in the hundreds of gallons. When the small bucket in your drawing overflows, all that water will be right next to and soon to be under your slab.
Can you put on a downspout extension that is 5' long and then put your rainwater collection tank there? Or trench from your downspout out a ways to your tank and bury the downspout the whole way?
Could you put in a decoy "decorative" pond that is really your rainwater collection tank?
Just some thoughts, good luck with it?
"Hundreds of years from now it will not matter what my bank account was, the sort of house I lived in or the type of car I drove... But the world may be different because I did something so bafflingly crazy that it becomes a tourist destination"
Michael, I hate living in an HOA. Have you checked with your city, county, and/or State laws to see if rainwater collection is allowed. In Colorado some of the "real government" laws allow for some permie things and it turns out that they trump the HOA rules.