I recommend you apply any finishing products before final assembly, but after any gluing or other permanent assembly.
Surfaces that are going to be glued together don't need (and shouldn't have) finish as this will weaken the bond, and the glue itself and adjoining wood should protect the wood (choose a suitable glue for the environment).
Surfaces that will never be taken apart but will not be glued (some joinery, for instance) probably don't need finishing prior to joining them. This is a gray area, and will depend on the joint. The primary goal is that exposed wood that isn't intentionally exposed will be protected.
However, other parts that are fit together using other fastening methods should be finished before assembly. Even small spaces admit moist air, and those spaces may expand or contract based on humidity, so may admit water or other environmental contaminants. Without protection on the interior facing pieces of the wood you risk visible damage over time in some environments.
Finishing as a step to preserve the wood in the environment it is going to be placed should help guide your decision as to when to finish. If you do it solely for looks, you may be happy with the results if you perform it after assembly, but time may show that protection should have been your goal during finishing, and not just looks.