Yes, given strict regulations. The police here in the UK are too lax, and the government has ensured they never actually do any crime fighting, just paperwork. My solution is this. Send all the paperwork police out on patrol and actually do something useful to prevent crime. Then, employ a shitload of admin staff to handle the paperwork. Then we solve two problems at once - crime rates fall and unemployment falls. Simple.
OT, there have been too many instances where innocents have been killed by armed police, such as Ian Tomlinson in the G20 riots and Jean Charles-de-Menezes on a Tube platform in London (he was mistaken for a terror suspect and was killed when he ran after they tried to arrest him). On the other hand, there have also been plenty of times when suspects have killed police and when the police would have been more effective had they been armed. So my response is that there isn't a simple answer, but given the circumstances the police should all be armed under strict regulation and control.