While some developers used special chips in their NES/Famicom games (Sunsoft and Konami in particular) I doubt that the songs from Bloodrayne Betrayal could be recreated through real NES hardware. They're much too complex. I've heard that even the songs from Mega Man 9 and 10 would sound slightly different/simplified had they been on a real NES.
I believe it can be done, though you'd need a co processor chip in the cartridge. A good example is the Double Dragon II NES game. It had a chip inside that essentially made the game a 16bit. That should be be enough power to process those chiptunes.
Also of special note, while making that particular Bloodrayne soundtrack, they were in fact using Sotn music as a stand in. Our buddy, Jake Kaufman himself is a Castlevania fan who was a tester for the game. Jake convinced the staff to give him a shot at making a soundtrack Castlevania style, and pulled it off pretty damn well.