Yes, it would be extremely expensive. The price of the plane for something like this ends up being only a fraction of the total cost of operating it. Between needing to source or machine parts to specification (many of which will be titanium) and the frequent inspections and maintenance needed it's a lot of time and money to keep a plane like this running.

Flying a GA plane is already a fairly expensive hobby... flying warbirds can be on a whole 'nother level of expense.