I'm having a hard time imagining how this would occur.
Stock splits are done to increase liquidity of trading. Because GOOG is ~$1000, and I can only purchase a whole share, I cannot purchase any Google stock if I have less than ~$1000 available.
With Bitcoin, it's simple to purchase $10 worth of Bitcoin (in most places), by just purchasing the equivalent fraction's worth. At the moment, the Coinbase spot price for $10USD equates to .0136BTC.
A 'split' for a US Dollar is a conversion to a smaller denomination, which does make it more liquid in a physical sense, but only for physical purchases. In the case of Bitcoin, i can already send fractional bitcoins wherever, and however.