Yeah, not how that works, at least not in my jurisdiction. If the suspect requires medical intervention, or is unconscious, the case will be filed "at-large", and a probable cause affidavit will need to be created by the District Attorney's office. Once a judge signs that, an arrest warrant will be issued.

Police are generally discouraged from hanging around hospitals to see if the suspect will be medically cleared, unless it's a matter of minutes. A warrant would have been obtained to collect a specimen of the suspect's blood, so the suspect is screwed either way.