If the US dollar crashed, would it affect bitcoin in any way?

[.m.]

Never say never And with Bitcoin - there is not a single person to kill

[Snorek]

You can have partial answer for Op's question. Yuan was recently evaluated and this as a result caused BTC price to instantly reach $600.
We know that planned davaluaton is not exactly a crash but you can see what is happening when currency is losing its value - bitcoin is gaining.

[elDano]

I can tell  you one thing that is really but really important and that is the us dollar cant crash anytime because everyone is using dollars in the world bitcoins can crash dollars cant.