Yes it applies to Bitcoin,
Many consider Bitcoin the Good money so would prefer to hoard it rather than spending
While Fiat is becoming more of as a means of exchange than a store of value.
Could something like this happen to Bitcoin?
In other words, are people starting to want to save their BTC coins so much that their value is lost?
No instead the value increases
When bad money drives good money, it doesn't inherently reduce it's intrinsic value just the circulation.
This may even make it scarcer and the value would remain same or increase based on the market perception.
It's a simple reasoning. If a coin is made of silver, it is easily worth 1$, but the amount of silver that this coin has is worth 2$. It's worth melting down that coin and selling the silver, rather than using the coin to buy something for 1$.
But, it explains the theory of Gresham's Law better.
That's why Fiat intrinsic value is lower than its nominal value to prevent such actions.
When people start melting silver it is removed from the market and what remains is a currency That's perceived to be inferior.
Inflation increases the likelihood of Good money leaving the market and held while the reverse is the case of bad money.