No, the police may not search without consent (of someone who could give consent legally; an owner or a renter/tenant or a family member who lives there and is not merely visiting) or a warrant, with two exceptions: if when they come, they see something which suggests a crime was or is being committed in the home, they may be able to search for the potential criminal or attacker, or for a weapon (so an unsecured weapon is not left unattended); and if they see something in plain sight, that is not a "search" (so if the respond to a heart attack and their are drugs on the coffee table, the police may take the drugs and use them in court). But otherwise, they many not do a general search without a warrant or consent, even when allowed in to respond to a heart attack or other medical emergency.