Do photons come out when electrons and holes recombine inside a forward biased diode?
Yes. Sometimes they do. That's called radiative recombination. There's other ways for electrons to lose energy and recombine with a hole. Those are the Shockley-Read-Hall (SRH) process and auger recombination. 

SRH is recombination through atomic trap's in the lattice. These traps are caused by impurities or defects within the lattice which create intermediate bands within the band gap. This converts the electron/hole energy into phonons (lattice vibrations/heat).

Auger recombination is when an electron-hole pair interact with another carrier (an electron or a hole) which increases the energy level of the already free carrier. This extra energy for the carrier is then usually dissipated through through phonon interactions (i.e. heat again).

If your electron-hole pair avoids the other two types of recombination, then yes, you'll get light shining from it. That's how LED's work after all.

See here for more info.