I don't have a clue how this could be an issue.
yeast needs sugar to replicate, unless you are pouring sugar rich waste down your drain, sans water, and letting it sit there for a week, you should be fine.
If you aren't rinsing it out regularly... do so.
In any case, there should not be enough biomass available to clog your drain, and yeast cakes are generally pretty soft to begin with.
I'm baffled.