The problem you have with creating the alerts in SolarWinds is that without the database, the alert engine cannot poll for alert statuses. We had a similar issue with MSMQ problems a while back (see here). Somebody came up with a crafty solution using VB and simple task scheduler, which can be found here. You'll probably find that in the event the database was unavailable, the MSMQ counts were high on the pollers, so monitoring for that condition outside of SolarWinds will be your solution, short of setting up a second SolarWinds with a different database server.
jangliss is right, it would be difficult to have SolarWinds alert when it's own database is unreachable. You'd have to have something else monitoring that database for connections/availability. The links he provided should help for this. Otherwise you may need to look at something like NeverFail for SQL to assist in monitoring/failing over the SQL environment in the case of an issue.