Yes it's possible.
You can set different thumbnail sizes on K2 settings between:
Item XSmall image width (in px)
Item Small image width (in px)
Item Medium image width (in px)
Item Large image width (in px)
Item XLarge image width (in px)
So you can select which size do you want to display on category view, category list view, item view, on tag view or on user page view.
Them if the user clicks on the thumbnail, it will display bigger size on popup window.
One thing that you need to know about K2 settings is that they are inherit or overruled.
screen.png
So if you select (e.g.) a different image size on specific item parameters, it will overrule the global and category settings.
Cheers