In principle yes, in practice the range is lower for most particles. Searches for microscopic black holes are the only example I know that comes close to the collision energy.

Protons are composite particles, and can be treated as collection of quarks and gluons each carrying some part of their energy. What we actually study (in most cases) are collisions of one quark or gluon from one proton with one quark or gluon from the other proton, so the effective collision energy is lower. The rest of the protons does some lower energy stuff we usually don't care about (LHCf physicists, don't hurt me).

In addition, many proposed particles would be produced in pairs, so you need at least twice their mass as collision energy. Sometimes they are only produced together with other particles, then you need energy for them as well. And finally the cross section (which tells us the probability of a process) is very low if you have just the minimum amount of energy required: It would mean all particles are almost at rest relative to each other, which comes with a very small phase space.

Combine all that and most searches are happening in the range of 100 GeV to 2000 GeV. We also look for particles with lower energy, but previous accelerators could look for them already, and particles with higher energy, but often we don't have enough statistics to limit theory models.

Going to 100-200 TeV collision energy would give us another order of magnitude in energy and increase the useful search range by a similar factor, yes. It's possible that there is nothing, but it would be unusual - so far we always found something new when increasing the energy significantly. Finding something not too far away could also solve some open questions about the particles we have found already, e.g. why the Higgs boson is relatively light.

Particles can be discovered even when the energy is not sufficient to produce them directly. They can alter properties of existing particles, like their production or decay modes. These indirect searches are harder to interpret (if they find a deviation from the Standard Model), but they can potentially find signs of particles far heavier than the collision energy.