No, it does not work that way. Performing an obligatory salah does two separate things:
- It fulfills the obligation of obedience to Allah
- It brings reward of performing a good deed
Praying in Masjid al-Haram has 100,000 times greater reward than prayer elsewhere (Ibn Majah). However it does not count as fulfilling the obligation of 100,000 prayers. Otherwise a person would just perform prayers for one day in Masjid al-Haram and then he would be free from the obligation of Salah for ~3 lifetimes. There would be no point in prescribing daily prayers.
إن التضعيف المذكور يرجع إلى الثواب ولا يتعدى إلى الإجزاء باتفاق العلماء كما نقله النووي وغيره فلو كان عليه صلاتان فصلى في أحد المسجدين صلاة لم تجزه إلا عن واحدة
This multiplication is in regard to reward and not in regard to being sufficient. On this the scholars are in agreement as recorded by Nawawi etc. Hence if two prayers are due on a person and he performs one of those prayers in Masjid al-Haram or Masjid an-Nabawi then it will not suffice except for one prayer.
— Fath al-Bari