I am curious about the Linseed application. Would that extend the life of the wood? And if so, by how long?

Linseed can only extend the lifespan of wood if applied correctly and re-applied every couple of month. A once-off application will not do much to preserve the timber over time.
An answer to the second question is entirely dependent on the regularity of the treatment.

On a side note, the main enemy of timber is a wood-destroying fungus that thrives in moist conditions. Avoid constant overwatering, and give the wood a chance to dry out from time to time. Doing this will extend the planter lifespan considerably.