Hi,
It's possible... It depends on how you configure your checkout.
The more you add stuff to it, the more the user has to click on elements.
If you have several payment methods, the user will have to click on one of them if he doesn't want the one preselected (and if you turn off the auto selection, it will have to do that click no matter what). Same for the shipping method selection.
If you have different fees for different payment/shipping methods, when you select another one, the system might not let you finish the checkout as the total amount changed (and thus you have to display the new amount to the customer before he can validate).
If you have different restrictions for different shipping/payment methods and that the available methods change when you change the address country, or the amount of products in the cart, a reselection of the shipping/payment methods might be necessary.
If you require a registration with an activation, the user will have to click on the link in the email to validate the registration before proceeding.
So if you configure a minimalist checkout, with the minimum things to do, it is possible to have a one page one click checkout but in most cases, the checkout will require several clicks, whether it is on one page or not.