As soon as you download the pc client, you can log into your account. One you log in, only 1 device can run at a time. But both will still be logged into the account. :)
As everyone mentioned, when you download Plarium Play on your computer you can log into multiple accounts through it. Just use the 3 elipses in the lower left hand corner to jump between them. You just can't run the game on both your phone and PC at the same time