Is running a portable air con unit on a highly loaded circuit going to be a problem?
The breaker will trip before the voltage sags, but if you're tripping breakers with any regularity, you have bigger problems.  

It's time to have a marking party and label each outlet/device for which breaker it is (give them names like Thor  Hulk  Ironman etc).  Get a Kill-a-Watt measure the actual amps of the appliance.  Then label that too.  Now you aren't flying blind.  Tell the family "no more than 16" or whatever. 

You will find that almost all the load comes from a very few appliances.  Don't make coffee with the A/C on, or whatever.