How cost effective is creating full text index for Fuzzy search?

Hello Team,

I have a requirement to have a fuzzy search on 1 each column of 3 huge tables (2 billion, 1 billion and 0.5 billion each). SAP recommends creating full text index for those columns with NVARCHAR datatype as we are not able to modify existing table structure to SHORTTEXT. Have anyone tried creating full text index and did analysis on how cost effective it is to create? Memory consumed by table shoots up by 2X if i create Full text index on only 1 column. Is it the expected behaviour? How much is the gain in search performance is observed here?

Thanks,

Akshay