Theoretically you can harvest yeast and eventually have its characteristics change over time, but those changes are random and slow. Unless you are basically always pitching and harvesting there is likely to be lags in production that will stress the viability of the yeast. Of course if you are planning a huge distillery this could easily be overcome.
As to harvesting/recovering yeast after fermentation this is common practice in the beer world, and could be done if you sanitation regime is solid. This would be easiest by far if your fermentation is done off the