If it included all of the metro area (West Memphis) they'd be even worse.
I would never consider West Memphis as part of anything regardless if it's in a combined statistical area or not. Different laws in a different state separated by a big ass river.
The crimes per capita would go down. There is roughly 650k people in the city of Memphis, and about 950k total in the county. The crime is way less in the county, and it would bring the crime rate down.