Of course EPR spectroscopy can detect triplet states. These can be either stable/persistent or transient. The former can be detected through continuous-wave EPR, while the latter usually require time-resolved methods. In general, EPR spectra of triplet states are more complex than S =1/2 spectra because an additional contribution to the spin-Hamiltonian, called zero-field splitting, must be considered. This is due to the anisotropic magnetic dipole-dipole interaction between the two unpaired electrons.
If the triplet is a photo-excited state, it is usually generated with non-Boltzmann populations of the triplet sublevels due to selective population by ISC from the excited singlet state or by other mechanisms. This translates in a spectrum that presents both absorptive and emissive transitions. Such spectrum is referred to as being spin-polarised.
If you are interested in transient triplet excitons you may look at this paper for an overview:
Article Delocalisation of photoexcited triplet states probed by tran...