Of course not.  In Europe, many currencies were replaced by the Euro, and the Euro didn't "rise" against these currencies to replace them.   The Euro got more and more participants, and replaced bigger and bigger markets, as new countries adopted the Euro, but the Euro didn't "rise" against these other currencies.  

Imagine that an imaginary bitcoin was emitted at against, say, $1 in the beginning, and that it had an emission scheme to keep it around $1.  (my proposal is to have proof of work that is about $1 worth, and can do as much proof of work as you want and emit as many coins as you want with that: if you are willing to burn about a million $ worth in proof of work, you own now a million coins ; if you want to burn a billion $ worth of PoW, you now own a billion coins).  Suppose that people like it, and start using it more and more.  Slowly, it starts to replace payments about everywhere.  The extra demand for the currency, to be able to use it (Fisher's formula) would make it rise in value, but that makes it more interesting to mine it, and it costs about the value of $1 to mine it, so people will mine a lot of it until it lowers again to near $1 value.  If it is less than $1 in value, nobody will spend PoW on it to make more of them, and none get emitted.  But if more people use them, more and more coins are in circulation.  The monetary mass, the market cap rise, and they replace soon most payments.  But nobody can get rich with it.  It is a currency.  Its value is stable (the value of about $1 of proof of work).  You can write a contract in it.  You know its value will remain stable (at least, will not deflate like crazy and become a rare collector's item).