If you think about how photons in a linac are produced you may answer your own question. In very simplistic terms a monoenergetic electron beam is directed into a target and a photon beam spectrum is produced which includes photons up to the incident beam energy. There are a number of pdf papers available on the internet that show example of photon spectra eg http://people.physics.carleton.ca/~drogers/pubs/papers/SR02.pdf. The simplistic answer is no, if however you have a poly energetic electron beam there may be a minor component of the beam which is a higher energy that the nominal energy and it may be possible to generate some higher energy photons.

it depends on the accelerators, 

http://www.ncbi.nlm.nih.gov/pubmed/24947967

The Varian and Elekta linac uses typically 6.1 MeV electrons to produce their 6 MV photons beam (Phys. Med. Biol. 57 (2012) 7599–7614). The 6.1 MeV electron beam will have ~50% of the electrons with a slightly higher energy and these elektrons will have small change of producing photons with a energy of 6 MeV.

As the question is stated the answer is no.

Photons are created by the bremsstrahlung effect where incoming electrons are attracted to the positively charged nucleus.  When attracted the electrons change direction and looses some of it's kinetic energy.  The difference in kinetic energy going out and coming in is generating the photon.  Therefore, the photon can never have an energy higher than the kinetic energy of the incoming electron.

The amount of kinetic energy lost by the electron is determined by the distance to the attracting nucleus.  For this reason the photon energy can be anywhere from close to zero to close to the kinetic energy of the electron.  This generates the characteristic bremsstrahlung spectrum where the mean energy of the photons is approximately 1/3 of the kinetic energy of the incoming electrons (assuming mono energetic electrons).