Is there a viable corn-only strategy for Puerto Rico?
With most games of this type, the key to winning is balance. 

My Puerto Rico strategy is to think of the game in 3 equal strategic phases


Phase 1 - get money
Phase 2 - get money/VPs
Phase 3 - get VPs


You can make a corn only strategy work, but only if you are playing against below-par players. But to get money in phase 1, corn doesn't really help you. To be able to make victory points in phase 2 and 3, a corn only strategy really stops you from preventing your opponents from shipping. Whilst a Wharf will help you, it will not be enough to win in most cases.

If you are playing against solid players, balance is the only option. I try to have 3 to 4 different goods being brought in, which gives great options for shipping and selling.