Subject: Can non-muscle human cells thrive using anaerobic respiration? How long?

I'm a high school biology teacher and ran into this question when talking 
about lactate fermentation in humans.  
If a person is submerged in water (preventing the replenishment of oxygen) 
can other cells -- particularly those keeping us alive like brain and 
heart cells -- continue releasing enough energy through anaerobic 
respiration?  I realize that this type of respiration is very inefficient 
compared to the aerobic type.  But do they have the ability?  And if so, 
how long would 2 ATP per glucose sustain brain cells?  

Re: Can non-muscle human cells thrive using anaerobic respiration? How long?