Yes but the yield will be extremely low compared too other energies.
The width of the radiation field depends on the diameter and divergence of the electron beam the distance from the conversion target.
The bremsstrahlung emitted from the target comes off at all angles and has an angular distribution that is strongly forward peaked so the radiation field is non-uniform transversely across the radiation field but radiation is being produced at all angles relative to the direction of the electron beam. As far as I can determine from the HERMES accelerator the target is very large compared to the systems that I am familiar with. The beam I expect is nearly as wide as the target. As the radiation leaves the target it diverges and expands laterally as you move away from the target. In linacs that are used to produce bremsstrahlung, the beam is mm's in diameter. To produce an isodose distribution that is constant across the field a flattening filter shaped like a cone is used to reduce the strong forward intensity of the field.
As far as I can determine HERMES does not use a flattening filter probably to maintain the high radiation field intensity that might otherwise be severely reduced by such a filter. Linac system with which I am familiar produces uniform fields up to 40cm wide at 1 m from the conversion target which can expand to 4 m wide at 10m from the target.
The size of the accelerator is determined by the size of the electron beam that must be produced to obtain the desired radiation field and the method of acceleration. Laser systems produce small electron beam diameters. Their advantage as I noted above is in their ability to produce high energy electrons in a small space.
You noted in your OP that a wake field accelerator produced 109 photons per pulse. This yield is extremely small compared to other methods of producing bremsstrahlung. Currently, the best wake field accelerators that have high yields per pulse are not useful for those applications that require high radiation fluxes since their repetition rates are too small. So replacing HERMES with a wake field accelerator is not yet feasible.