You can manage SSO with the Web Client, so if you do not want to use the command line to see if all your AD domains have been automatically discovered you will need to install the Web Client after SSO (not before, as it does register a solution user to SSO).
You will not need to register vCenter server to the Web Client like in 5.0, this will be done automatically by registering all components to the same SSO instance.
VMware Product Interoperability Matrixes is your goto point when you want to check database compatibility. vCenter 5.1 U1 is compatible to SQL 2008 R2, 2008 R2 SP1 and 2008 R2 SP2 with some exceptions on the datacenter edition. More details can be found in the interop matrix.
For the host agents no downtime should be required, performance should also not be affected, except maybe the network traffic when you got alot of hosts. If you don't do the update all hosts will show as disconnected until you manually reconnect them which will update the agent anyway.