The short answer is no.
The longer answer is that projects started on the mobile app can be imported into the desktop version, but not the other way around.
Also, each platform requires a separate license so you'll need to purchase the mobile app and also PD365.
For the desktop version, Windows and Macs require separate licenses, but you're allowed to install PD365 on a desktop and laptop as long as they both run the same OS and you don't use them simultaneously.