Although you can include Swiss (LX flight numbers) on the OneWorld Global Explorer fares, you don't earn any QF Status Credits on Swiss flights. You can only earn QF SC's on QF, OneWorld, Air Pacific and QantasLink flights.
Also note that you only earn QF FF points on some Swiss flights. These are listed in the QF FF program terms and conditions as:
Points can only be earned on flights operated by Swiss with an 'LX' flight number within Switzerland, between Switzerland and Asia, between Zurich and Frankfurt and on codeshare flights with an 'LX' flight number operated by Qantas between Australia and Asia, Frankfurt and Sydney, and Frankfurt and Singapore. Asia is defined as Bangkok, Denpasar, Hong Kong, Jakarta, Japan (Osaka and Tokyo), Singapore, Beijing and Manila.
So yes you can use Swiss for LHR-ZRH-BOM and you will earn QF FF points on the SRH-BOM segment only. No QF FF points for Swiss to/from North America.