Yes if you should check the mining pools address you'll see the coins sitting there however it doesn't have an input and output since the coins were not spent by a transaction. However the miners coins will have a transaction hash because it is a reference to the origin of the coin and when I mean origin I'm referring to POW and timestamp data.
The POW data tells where the coins come from this is to prevent any coin from being faked and spent on the network. The timestamp shows the time and date about the origins of the coins.