I don't think there's a strong connection.  The historical value of gold derives from its physical properties including:

1.  The fact that it is the least reactive metal.  It can be kept in storage for thousands of years and never rust.
2.  The fact that it is appropriately scarce.  Storing the right amount of value in other metals (excluding silver, which is also traded as a store of value), is difficult.
3.  The fact that it is shiny and beautiful, it's a show of wealth like in jewellery.

Those intrinsic aspects of gold will remain and so its value will never be very low.  Unlike gold, Bitcoin is easily replicable in the form of altcoins, but these generally do not get much traction unless they are hugely different to Bitcoin, so it has value in its scarcity and security.