I don't have a standby database to test this with, but I just mounted a database but didn't open it.
When I tried to connect as "normal" (not SYSDBA), I got the expected "ORA-01033: ORACLE initialization or shutdown in progress" error.
When connected as SYSDBA, I got a few "ORA-01219: database or pluggable database not open: queries allowed on fixed tables or views only" errors, but after that, Toad allowed the connection and I was able to open an Editor and run queries against the V$ views.