In principle, yes. The relevant equations can't be solved exactly for any non-trivial molecules. But there are a large number of different approximation methods

In principle, yes. The relevant equations can't be solved exactly for any non-trivial molecules. But there are a large number of different approximation methods, which boil down to a numerical optimization problem that converges on a bounding value. These methods generally don't scale well, however, so as the size of the system grows, the approximations that can be successfully solved quickly grow too coarse to be useful. There are also a lot of simple heuristic methods that a chemist can employ that don't require collaboration with a theorist, e.g. particlar chemical "motifs"/"functional groups" generally have a Raman resonance at a consistent frequency that is affected only slightly by the surrounding parts of the molecule (and the general direction and order of magnitude of that shift can also be approximated heuristically). Finally, there are enormous catalogs of recorded spectra for a huge range of molecules at e.g. the NIST webbook (http://webbook.nist.gov/chemistry/ http://webbook.nist.gov/chemistry/).