If miners can be encouraged to run SHA256 for something more profitable than Bitcoin then bitcoin will die quickly, it's a winner takes all game.
In a nutshell, there is a chance that a different form of adaptive money might outperform Bitcoin and hi-jack its network.
This happens all the time. PPC is often more profitable to mine than BTC, for example. Miners who bother will shift to PPC, mine the PPC, then promptly dump it into the market to increase their BTC supply. Eventually PPC sinks and they switch back to mining BTC. Lately this doesn't happen often because (1) BTC+NMC mining is rarely worth less than PPC mining, and more and more people mine the combination, and (2) it's such a small gain, that even a tiny friction will make it a net loss, and who can be bothered?
The net effect of competing currencies has always been to increase the value of bitcoin. If you want to buy DOGE, the easiest way is to buy some BTC, then exchange. When you mine DOGE, you're probably going to dump it in order to buy BTC. The same thing would happen with govcoin or corpcoin if it could be PoW mined. AUR is the most akin to a govcoin of all the alts so far. It's basically an ethnocoin. Let's see how that plays out. My bet is that it will get dumped for BTC just like every coin before it.