I started a second game just to see what certain cheats would do for me and to pretty much just mess around.

I entered the cheat - player.additem 00023B62 1 100 (it is the Enclave power armor)

Now when I get out of the console command, it says that one has been added and I can see the weight of the item I wanted but I don't have the item in my pip boy. Where do these item get put when you use the cheat?

Using the console can be a bit of gamble. On some rare occasions it can bug and completely mess up your current game. In response to your question, for 100% health you don't need to put anything after the quantity (player.additem 00023B62 1 is fine) and there seems to be some confusion with the base ID you've given. GameFAQs and a few other sites says 00023B62 is the code for the Enclave Power Armour, but the Fallout wiki says 0004443e is the code. On the few occasions I've used the console I used the base ID's in the Fallout wiki and none of them have been wrong, so either the base ID you're using is wrong or its simply the items health you put down is confusing it. You only need to put the items health into the code when you want it at something less then 100%.