You could think of it as a short loop antenna, with some capacitive loading on the gap. The gamma match is equivalent to a lower tap, or a coupling winding, and the capacitive hat gives some voltage radiation but isn't at the highest voltage point so it won't be quite as effective, but that's all just a matter of matching.
Although the structure is rather complicated, the physical size is too small to have a radiation pattern anything different from a traditional monopole or loop.
I would guess the bandwidth is on the order of 10% or less, and there will probably be secondary peaks at much higher frequencies, where the length of the gamma match or tuning leg become characteristic. Probably at 1/4 to 1/2 wave long and multiples thereof. At those frequencies, the capacity hat will act like a ground plane. And, of course, you'll have more complicated radiations patterns, depending on the phasing (electrically and by physical distance) between those elements.
Tim