Clearly 1 Corinthians 12:13 teaches that each individual believer has been baptized spiritually, above and beyond baptism in water. But I don't think that's what Romans 6 is referring to. I think Romans 6 is referring to water baptism.
Now, I'm sure that each believer, baptized or not, is united to Christ in His death, burial, and resurrection. Galatians 2:20 brings up our union with Christ, with no mention of baptism. So I'm not saying that a believer who isn't baptized in water hasn't died with Christ.
But Romans 6–8 is all about our life down here, in a wicked world, in fallen bodies (Romans 8:10). It's not about our life in the world to come, nor about our place with Him in heaven. It's dealing with our practical walk as those united with Christ in this life, and that's what baptism is all about.
Notice that the issue in Romans 6 isn't what God sees, but what we see. It's about our reckoning, not God's (Romans 6:11). And when we're talking about what we see, we're talking about an outward reality; we're talking about baptism.