Do not trust the numbers in the box here, mobafire does not calculate for the bonus damage from most of the items used here. The mana damage bonus is 126 magic and 42 AD, and the bloodthirster bonus when stacked is 30 AD and 6% each, making actual AD 280 - 300 (depending on mastery/rune preference) and actual life steal 36% (12 base for each bloodthirster + 6 each stacked). Endgame you should deal around 300 Ad + 200 AP damage per auto-attack, so around 500-600 damage normal, more on the initial hit. This level of damage, combined with how "cheaply" you can build it early and thresh's normal support abilities allows you to be an effective secondary damage dealer, bursting down the hp of an enemy champion to allow your lane carry to get an easy kill.

Pros:

In short, the pros are pretty obvious, thresh is a natural support and the damage from this build is massive, allowing you to be both support and AD tank. Around midgame once your muramana builds you'll often be able to chain and one-two hit a champ to score an easy kill for your carry on all but the tankiest of champs. You will get a LOT of support kills from this build, and you'll keep buliding off souls for more damage and armor the longer the game goes on so you can allow your ADC to take the last hit while not losing much yourself.

Since thresh naturally gains armor and ap from souls you dont have to worry about items for that as well so long as you keep farming and stay near enough to pick up souls (dont forget the lantern picks them up, so you can toss it in if it's too dangerous to pick them up there yourself!). If the enemy team is using a lot of AD this is very good as thresh is extremely tanky late game vs AD based champs, so even when focused you'll often either escape or take most of their team with you.

Cons:
Most players after the first few kills will start focusing you first to keep you from bursting them down, and as you have to build muramana early due to the way it upgrades you will have somewhat hp until fairly late game (more than most champs, as thresh is naturally pretty tanky, but not enough to midgame tank with no defensive/health items).

Another downside is you NEED to build the mana early on the goddess tear/manamune so the second you have the gold you need to be able to fall back and buy, this means while you don't need as much you really should take some CS early, so make sure your bottom carry is aware of this and doesnt expect you to be pure support. If you can't get the gold and fall back to buy early you miss the chance of the easy kills midgame once it builds, and while it's still effective lategame midgame is where that damage boost is extremely overpowered.

The mana itself is an issue. Muramana's damage boost works by consuming your mana, so essentially every auto attack is now a spell consuming it while it's active. (though silence has no effect on it) This means you need to fall back to base to refill mana when low, as when you run out of mana your damage is halved and you become next to useless.

Another major downside is you need every item slot for damage boosts but one, so you either get health or defense, so unless you sacrifice the warmogs you have no great defense against magic attacks or spells/stuns. If you have a good tank eating the hits for you it shouldn't be a big issue, but against champs like fiddlesticks you might want to sactifice the extra hp for banshees veil.

While there are major downsides to the build the upside of bursting down multiple enemy champs in very few hits to allow your team to finish them off IMHO far outweighs the downsides.