Is it worth training the blacksmith?
Solution 1:
You can make a very strong case that for the majority of users buying gear from the AH will put you further ahead as opposed to levelling up the blacksmith.
However, this relies on the prices in the auction house remaining low. This should be a safe, long term assumption as the supply should outpace the demand assuming people resell items they purchase.
The best gear that the blacksmith produces is certainly being hoarded by those who have invested the time and effort to generate it or will be offered for sale at an enormous price.
In the short term, yes, you can do better in the AH under the current economy.
In the long term, dependant very strongly on your luck in crafting equipment with the stats you are hoping for, the blacksmith may become your better source of equipment as the best Legendary items will almost certainly be absurdly priced.
Crafting equipment has always entailed some risk. In Diablo 2, the best players would hoard perfect rubies to try to create "Blood" gear (items with strong life leech). If your build calls for such a piece then it may be the small advantage you need to start succeeding in Inferno.
Many won't want to do this but will benefit from the few who are doing it. If they're looking for dex gloves and you want int, their failures are your opportunity to buy.
Solution 2:
Its important to keep in mind that the Blacksmith is Diablo 3's version of gambling from Diablo 2. It is meant as a way for you to use gold that would otherwise go unused. Most of the time, that gold will be wasted and you will get nothing out of it, but every once in a while, you might "hit the jackpot" and get a really good item.
Training the Blacksmith essentially allows you to give up some money in order to increase the size of the jackpot. It is an "entry fee" in order to play for the big bucks.
With that said, training the Blacksmith is only useful if you are at a point where gambling is a good use of your gold. Given the prices on the auction house for low and even mid level gear, there's no reason to be gambling at lower levels. You can get a sure thing that will help you level up for a tiny fraction of the cost.
Once you reach higher levels, the jackpot gets big enough and the auction house gets expensive enough that gambling becomes a reasonable way to spend your money. At this point, you should level up your blacksmith. This has the added side benefit of unlocking the blacksmith for all future characters, meaning you can use him at lower levels if the auction house were unable to supply your needs for some reason.