First Off, yes, its pretty much instantly now, I have access to run fingerprints from my phone!! Granted most local cops don't have this ability, but fingerprints come back in seconds now, it is all automated.
Secondly, do you really think that someone who knew enough not to have an ID on him when he committed the crime, and had a false identity ready to go for the police, has never been arrested before?
I'm sure whoever it was, has been arrested before and most likely had warrants under his real name, hence to move to "Lucky".