Just looking at the beam energy and peak power for the LHC, 360 MJ and petawatts, respectively, dumped in about 100 µs, would this be sufficient to do useful fusion experiments?
The simple answer is No.
Fusion happens at nuclear energies between particles to be fused, i.e. MeVs, because it is at the framework of nuclear bound states.
LHC particles start with energies of TeV, so particle particle interactions are way over any nuclear bound state levels. Even if one accelerates deuterium nuclei the phase space is way over the fusion levels.
Nuclear-fusion experiments have been extensively performed with accelerators in the last decades of the 20th century reaching the proton drip-line. Today they are still object of interest allowing the study of superheavy elements.
However the energy of the LHC is way too high. At that energy scale you go in the regime of quark-gluon plasmas and the nuclear structure is completely destroyed. It is impossible to run the LHC down at some MeVs: the field quality of its magnets would be terrible, moreover an effect called space charge would destroy the beams in probably less than a single turn.
If you are interested in energy-production-oriented nuclear fusion, then you need a lot of particles at quite low energy which is the opposite of the LHC. There exist very specific magnetic designs to obtain that characteristics, the most promising being the Tokamak, the Stellarator and the Reversed Field Pinch.