I almost never takes me more than 15-20 minutes from stepping off the plane to being on the train platform, regardless of the airport in Japan. I do have the automated gate pass for immigration, but unless you're arriving at peak times it doesn't save much time, just avoids entry and exit stamps which greatly extends the life of my passport. Unless something goes drastically wrong, you'll have heaps of time waiting for that 7:27am train.

There is no reason though to purchase a ticket before you arrive, trains have plenty of capacity unless peak Japanese holiday periods. Actually I don't even know of a way to purchase tickets ahead of time outside of Japan, but you can make reservations for tickets on some lines. In these cases you don't actually pay until you pick up the ticket anyway and the reservation automatically cancels about 10 minutes before departure if you haven't picked it up yet.