I think the answer is no, and maybe.
! atm exerts 101 $\frac{kN}{m^2}$
Since sound is a time-varying pressure value about a mean value -- let's assume 1 atm -- the rising pressure would exert an equal force on the ground as on the vehicle by displacing the air.
To get enough force to lift an object you need to counteract gravity and then some. As @Slarty observed that would require a huge impulse to achieve. But, it would also displace the air, leaving (we'll assume for sake of simplicity and illustration of the argument) 0 atm or a vacuum beneath the vehicle. Atmospheric pressure would push the vehicle back down and the sonic transducer wouldn't have any air to create the next impulse until the vacuum dissipated.
The sonic impulse would generate such a force that the air would accelerate to speeds faster than the speed of sound -- you are talking tremendous power here. But the filling rate of the vacuum can only proceed at approximately an average of the speed of sound. This because the speed of sound in gases medium is geometrically related to the average distance a molecule can travel before colliding with another and its average velocity due to temperature and pressure.
So if your vehicle (transducer, power source, payload, etc) weighed 1 kg. You'd need to generate an average positive 10 N force to keep it aloft. (rounding to avoid math) Assume the pressure under the vehicle varied between 1 atm 0.9 atm, you have a 10 $\frac{kN}{m^2} force pushing you down on the negative or off cycles of the sonic impulse. You can't really get the values close to equal unless you make the area microscopic or the mass very tiny.
But, if you did have the power to do it. YOu could easily use it to heat the air like a ramjet and give yourself a continuous lift.