Buy an app on mobile, but confirm (password) on desktop via email?
Not that I know of, why not:


Install your password manager app on your phone (I use LastPass) and have it auto-fill your password (or copy/paste)
If you are going to be purchasing the app from your phone and were going to your desktop anyways, instead just go to Google Play via your desktop and purchase it from there, and have it then download to your device