Unfortunately, no. The offer is only available for new subscribers purchasing a Backbone One.
***Valid for new Xbox Game Pass members only. Purchase must be made through a Backbone or Microsoft storefront to qualify for 3-month trial. All other purchases through authorized retailers will receive a 1-month trial. Credit card required. Unless you cancel, you will be charged the then-current regular membership rate when the promotional period ends. Terms, exclusions, and streaming limits apply. Xbox Cloud Gaming (Beta): select devices and regions. Upon redemption existing Gold memberships will upgrade to Ultimate at a conversion ratio. Game catalog varies over time, region, and by device. See xbox.com/gamepass. Limit: 1 per person/account.