Prius V Engine Rattle + Coolant loss

it sounds to me like the answer is no.

welcome!
you likely have the clogged egr circuit problem that many experience around 100,000 miles or later.

it sounds like this has caused the head gasket to start to fail, which will call for a new one, or replacement engine or car.
toyota has not published anything that i am aware of regarding this problem, and the dealers are ignorant of it.

but there are tons of threads here detailing the problem and solutions.

 

Cool/cold morning starts often evidence water vapor, a combustion by product.

Coolant level is temperature dependent. How are you measuring 'loss of coolant'?

Brief rattling/chattering on startup is widely reported, and could be residual fuel in the intake plenum. That could point to injectors, or to timing.

 

uh-oh

 

There was another in the gen3 forum that had coolant blow past the pressure relief valve in the reservoir cap. It turned out to be a bad thermostat boiling the coolant and not a headgasket. Where did the coolant go? Out the exhaust or out the reservoir?

I'd refill the reservoir, run the engine in maintenance mode and observe where the coolant is going

Pixel XL ?

 

Totally empty coolant reservoir and Toyota couldn’t tell you why? Wow they sound useless to me. It’s impossible to diagnose from here but it sounds like the head gasket has blown leaking coolant into 1 or more cylinders causing engine rattle and the white smoke is probably water vapour. As the car sits over night more water is able to accumulate in the cylinders which is why it’s worse in the morning.
Have you ever had the water pump replaced?
I just did mine and found the plastic on the impeller magnet had cracked and swollen causing the impeller to intermittently stop spinning. I saw the temp light flicker once and the engine hesitated and rattled once then the next day i had the engine light on dash with water pump codes. There is little warning before you overheat a prius. I got lucky

 

If you are going to throw the car away then you have nothing to loose. There is a product called chemiweld. The instructions need to be followed exactly as directed. This product can fix a blown or even cracked head for up to 5 years. If your not confident with cars ring around and find a mechanic that is familiar with the product. It would be preferable to find someone who has had success in the past with this product. I have used it in cars that were not worth repairing and it has lasted for years. Just make sure you fix the original cause the overheating like water pump or thermostat.
Good luck mate

 

I recently purchased a 2012 V that was burning coolant, engine ran sometimes and sometimes it came to a dead stall upon start up. Had coolant in oil and white smoke. I removed head and found about 1/4 of coolant and a spotless clean combustion chamber on #1 cylinder and a bad head gasket. Now here's the question, how many people would just do necessary maintenance to replace head gasket and be on their way? Luckily, I decided to look at rods and sure enough, #1 was bent. So keep this in mind, I think this is a 13to1 compression motor, not much room for error

 

fortunately, the labor involved in replacing the gasket opuses many to just skip that option and get a low mile salvage