I put the deck together and ran it a while last night, and it went better than I expected. I'm 3-star Diamond, and was having a blast beating people packing all-star rares like Argent Commander or popular legendaries like Sylvanas Windrunner..
The deck is very much control-based, with eight single-target removal spells (Shadow Word: Death/Pain, Holy Smite, Mind Control) and two Holy Nova. That's a third of the deck dedicated to removal. The remainder has a few minion health boosts and is packed with workhorse basic minions like Chillwind Yeti and Gurubashi Berserker and card drawing utility minions in Novice Engineer and Northshire Cleric.
It's important to keep your larger minions healed up, as your win condition is likely an ogre or angry Gurubashi to the face. It's debatable as to the effectiveness of Shadow Word: Death, as it can sometimes be a dead card. Many players have realized that 4-attack minions are the hardest for priests to deal with and capitalize by running as many of them as they can. That said, players also often run Shattered Sun Cleric, Dark Iron Dwarf, and Defender of Argus (all of which booth the stats of other minions), putting their 4-attack minions into Shadow Word: Death territory.
Being control, the deck is also rather slow and can be overwhelmed very quickly by aggro rush. If a warlock or rogue ends up with the Coin, you're probably in for a troublesome start that you may not recover from. Also, you will curse Faerie Dragon's existence because your only means to remove it is via combat or Holy Nova.
In an upcoming patch, Mind Control is going from eight to ten mana, making it a truly late-game spell that won't allow you to cast anything else that turn. This will be a significant problem for this deck, and I'm uncertain the deck will be very viable after that. Mind Control is a bomb however, and can be a huge menace in Arena play, thus the cost increase. If you want to try this all-basic deck, I suggest doing so ASAP.