Will insurance cover a total loss to a full coverage auto when the car is covered by a personal policy yet the car is titled to the owner's company?

Not sure I totally understand your question. Are you both the owner of the company (and the car), the car is titled to the company, but have the car insured as a private/non-business auto? What were the questions on the application? They ask about business use, if those weren't answered honestly there could be a problem. Or are you saying the company ou work for owns the car, but you have to carry insurance on it? Same question about the application would apply. Please be more specific and I'm sure I could be of more assistance.