The do make ultrasonic injectors (from Sono-tek) and they have some very interesting qualities:
Better Control of Spray Shape
Ultra-low flow CapabilitesThe spray can be controlled and shaped precisely by entraining the slow-moving spray in an ancillary air stream. Spray patterns from as small as 0.070 inches wide to as much as 1-2 feet wide can be generated using specialized types of spray-shaping equipment.
Drop-Size Range SelectivitySince the ultrasonic atomization process does not rely on pressure, the amount of liquid atomized by a nozzle per unit time is primarily controlled by the liquid delivery system used in conjunction with a nozzle.
The flow rate range for the entire family of Sono-Tek ultrasonic nozzles is from as low as a few microliters per second to up to about 6 gallons per hour.
Depending on the specific nozzle and the type of liquid delivery system employed (gear pump, syringe pump, pressurized reservoir, peristaltic pump, gravity feed, etc.), the technology is capable of providing an extraordinary variety of flow/spray possibilities.
In general, the drops produced by ultrasonic atomization have a relatively narrow size distribution. Median drop sizes range from 18-68 microns, depending on the operating frequency of the specific type of nozzle. As an example, for a nozzle with a median drop size diameter of approximately 40 microns, 99.9% of the drops will fall in the 5-200 micron diameter range.

Well, I thought that this isn't exactly a fuel injector, but sure enough I found a patent for a "ULTRASONIC UNITIZED FUEL INJECTOR WITH CERAMIC VALVE BODY"
An ultrasonic fuel injector (30) for injecting a pressurized liquid fuel into the combustion chamber of an internal combustion engine that uses an overhead cam

So, they definitely exist, but do they really work? Would they be any good for F1? Are they legal?
Certainly, 18-68 microns is very, very small for a droplet. I don't know how it compares to diesel fuel injected at 1000+ psi. but it sounds small to me. So, it seems promising.