No, you cannot change the defaults. Yes, you can create a board as a "starting point", or Template, and go from there. This template board can contain "anything" that does not relate to a netlist. Start a new board with the defaults, change all the settings you require for the template, save the resulting BRD file.
Within PCB Editor: 16.5 and on: File>New, there is a template button to browse for a template and a User Preference to configure as the Template file source. Previous releases: copy the "template" and load the Logic into it.
Schematic driven: All versions: I think that both the HDL flow, and certainly the Capture (CIS) flow, allow an "input board" to be specified as a starting point to load the Logic into, Export Physical for HDL and Tools>Create Netlist for the Capture CIS flow.