I would not splice if by that you mean cutting the insulation and twisting the wires together, using wire nuts or one of those automotive splice connectors that cut through the insulation. Your black wire is likely to be 10 or even better 8 gauge wire. As you surmised the +12V line between the converter and the + battery post is electrically the same. If given a choice I would crimp a correctly sized ring terminal to the end of the black wire and secure it to the bolt on the + battery post clamp. If not practical I would crimp on an appropriate connector to securely attach to the converter battery output terminal. Don't forget that fuse.
Air Safe Hitch, Reese Dual Cam 800#, Centramatics