Gresham's Law technically applies to nonidentical versions of the same legal tender. That's not applicable to Bitcoin, because there is no material difference in the manufacture of individual Bitcoins, and nobody is forced to use or accept it.
But to think this through, maybe there would be three components to the dynamics of such a theory.
1) Bitcoin will continue to vanish as holders die, forget about their bitcoin, or lose access to their wallets.
2) Up until a certain point, this will cause the value of Bitcoin to increase, as reduction of the Bitcoin supply is deflationary. Those who recognize that this deflation is occurring will hang on to their Bitcoin, because of the expectation that their holdings will appreciate in value.
3) After a certain point, people will realize that much of the total Bitcoin capitalization has been lost/forgotten, and they will be in a hurry to use Bitcoin (sell it for goods) before their holdings become too large in proportion to the total non-lost capitalization still in circulation. Proportionally large holdings are worthless if they cannot be liquidated or used. (Similarly, imagine a currency with two holders, half each; neither is incentivized to accept large transactions because if one sells out, the other is left owning the entire currency by himself.)
I predict that people will realize that Bitcoin is incapable of robustly facilitating a global amount of transactions without centralization in banks/hubs/wallets/exchanges, thus defeating its stated advantage of immediacy and anonymity, far faster than individual coins fall out of use.