Is it worth shopping for rates?

[Marty Gold]

Am I correct to understand that a bank or credit union will not negotiate their current set mortgage rates for a small time rental property purchaser?  

I do believe some banks may have slightly different rates.  Do banks also have different closing costs (is that something which can be known prior to presenting the details of a property)? 

Do people shop between 2-5 banks and try to find the best rate or are they all the same and thus, not worth the time to shop around?

Thanks