Is there a way I can generate a SPICE netlist equivalent of my schematic?
Yes. With your schematic loaded, go to the File menu, click on Translate, and select Schematic to SPICE Text File. This command will let you convert your schematic to a netlist in a few different SPICE formats such as PSpice.
Note that there can be items in the schematic that do not have a SPICE equivalent and thus will not be part of the netlist.