You sure can, but I'd put a fuse/ fuse link in there. big enough to handle the alternator, and small enough to protect the wire.
What did the rewire guy do with the bulkhead connector? did he rebuild or eliminate it? or just hack into the old one? I'd make sure the terminals were OK becaus you still have to pass all the current feeding the accessories, etc, through that connector, if present. the ammeter, if connected won't work anymore, you'll need to add a voltmeter
What is the rated capacity of this "1 wire."