No, each Dynatrace AppMon server will need it's own database to be used as the Performance Warehouse they cannot share them. These databases can be hosted on the same physical machine but they need to be unique per server.
+1 for what James said.
You can however use the same PW for two AppMon Servers, just not at the same time. For example in a failover situation. It's up to you to implement the shutdown of AppMon Server1 before connecting AppMon Server2 to the same PW.