Purging Cornies with active fermentation

I have rigged up my actively fermenting fermenter to two cornie kegs set up in sequence with the second keg’s in post running with a line out to a starsan bucket.  Does anyone have an idea how long it might take to purge all O2 from the kegs (with CO2 replacing it)?  I want to purge several cleaned and sanitized kegs in this manner, two at a time.  The fermentation is rolling from a batch I made yesterday and I want to take advantage of the free CO2 as long as it might last in this active fermentation state (Omega Hot Head yeast, if that matters).

Thanks in advance - Cheers!

http://www.lowoxygenbrewing.com/brewing-methods/kegging-care-guide-purging-transferring-stabilizing-finished-beer/

Sounds like I will need to spund these kegs…I thought I could get ahead by purging and storing.  So,assuming closed transfer, is there enough oxygen left to spund with these semi-purged kegs after fermentation completes on the current batch?