The electrical situation in our house is that almost all of the outlets are on the same circuit/breaker and when there is too much load the breaker will trip. We need a new cable run to part of the house to separate the outlets... It is warming and I decided to plug in the portable air conditioner. I am concerned that if there is too much load in the house the voltage supplied to the portable air con might be too low, which in particular I know motors don't like... In this situation could the voltage be low enough to cause problems or will it be ok until the electrical upgrades are done?
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.