Not if you are using "Turbo..." yeast, I suspect they paralyse the yeast so it cant reproduce (SO2).
The other problem is that the very high alcohol in the all sugar washes would be a powerful mutagen and the yeast would become very unreliable very quickly.
When people make malt washes for whiskey, or fruit washes for brandies (marc) the alcohol content of the wash tends to be much more beer like ~5-10%, go too high and you start to get too many fusels and other off flavours.
Yeast from these ferments could be harvested and reused just like beer yeast. It would be important to make sure that your yeast received enough of all the trace elements and lipids that it needs, or it will go out of bounds pretty fast.
Every type of spirit making has its own yeasts (malt, grape juice, fruit juices, rum...) they are just as important to the finished product as brewers and wine makers yeast is to them.
Personally I think you shouldn't **** with yeast unless you have a PhD in the subject, its way more complicated than people realise - especially if you are trying to keep a pure strain preforming to speck.
You know disusing distilling is verboten on AHB, go to the distilling forum if you like, but specialised yeasts are an interesting subject. I have made an Ale with Whiskey Yeast (working on an Innis and Gunn clone - haven't seen that for a while), also used it in a Nessie clone, and a specialty Calvados yeast in an experimental cider (yum).
Mark