Pixel 2, which should be the same thing - no. I always have mine on when charging (Magisk with MCS, so it stops charging at 80%), and it's never shut off. It charges just as quickly with Pie as it did with Oreo (and is discharging a lot slower).
Yes. I had the same thing on my pixel 2xl. I have about 5 different chargers and at one point none of them would charge it and some of them would cause the phone to shut off. Even the OEM charger. I called Google and they sent a warranty replacement. All is good on the new one