Can you set password to open Quicken app?

You can set a password on the data file, which is a separate option from the Password Vault.
If set this password you enter it to open the data file.

If you use the Password Vault you have to use a password there too.

There isn't any option to ask for the Password Vault password when you start.  You get prompted for it when you start something that requires it like downloading transactions or syncing with Quicken Cloud.  There is an option to start One Step Update when you open the data file.
It is in Edit -> Preferences -> Startup

Note if you use scheduled updates you can't use a data file password.