I mean, if they had PC or ARS to charge or detain him on some other crime, sure. In the former case they could start putting him through the system and all the trappings that come with that. In the latter they'd have an hour or so at most.
You know though, it's funny, hearing all these internet ditektivs talk about what should have been done in this case. No wonder they all hate cops. If police agencies actually did investigations the way everyone seems to think they do, I'd hate the police too.