2013 Toyota Prius p011b

Absolutely. While it is possible for oil and coolant to mix from a leaking head gasket, that is not very common. 99 percent of the time combustion gases, which are under very high pressure, gets forced into the cooling system where it often causes overheating because those gases can pool under the thermostat. Thermostats have to be hit with hot liquid to open. Hot air won't do it. When the thermostat stays closed, no hot coolant can flow to the radiator to give up its heat.

At the same time it is typical for coolant to get sucked into the cylinder during the intake stroke. It gets burned and goes out the exhaust where it causes white smoke. The symptoms can be overheating, white exhaust smoke, coolant loss, air bubbling in the coolant reservoir, or any combination of those.

Actually, you're approaching this the wrong way. The Engine Computer is constantly monitoring a lot of sensors and operating conditions while you drive, and when it detects a problem, as yours did, it sets a diagnostic fault code in that computer, and if the problem could potentially have an adverse effect on emissions, it will also turn on the Check Engine light. The place to start is to read and record those codes, as it appears your dealer did. Without the code(s) to direct the mechanic, it would take him many weeks to test each individual circuit to determine what is wrong, and even then there's no guarantee he would see anything wrong if the problem is intermittent and not acting up during the test.

There's over 2000 potential fault codes that all mean very different things, but it's important to understand that those codes never say to replace parts or that they're bad. They only indicate the circuit or system that needs further diagnosis, or the unacceptable operating condition. You can go to this page:

https://www.2carpros.com/trouble_codes/obd2/P0100

if you'd like to get an idea of the types of things that could be involved. It's hard to say a cylinder head gasket is leaking just based on fault codes, so I'd bet the dealer did more tests than just reading the codes, or there is some common problem and they're basing their diagnosis on the fact that they've seen the same thing many times before. I, myself am not aware of any common engine problems with your model, so you might consider getting a second opinion before having any repairs done. I don't have a listing for this fault code so I can't make any judgement on what might be causing the code to set.

It IS real common today to have leaking head gaskets on all car brands but much of the trouble is caused by a failure to replace the antifreeze regularly to get the acids out that develop, and to get new additives in that wear out in about two years. You car is too new to be concerned with corrosion yet, and the mileage is rather low too. Still, on some car brands, we see leaking head gaskets in less than 50,000 miles.