quoted identifiers on filtered indices
Parameter values containing double-quotes are not affected by the QUOTED_IDENTIFIER setting within the proc unless you use dynamic SQL. The setting affects how the T-SQL statements are parsed. 

As long as the T-SQL proc code encloses string literals using ISO SQL standard single quotes like your example, you can safely recreate the proc from a session with QUOTED_IDENTIFIER ON to persist the setting as object meta-data. The QUOTED_IDENTIFIER ON setting will be used at run time and allow you to use filtered indexes and other SQL Server features that require the ISO standard setting.

I recommend you ensure both QUOTED_IDENTIFIER and ANSI_NULLS session settings are ON when creating creating objects to avoid surprises later.