No. Learned this the hard way after purchasing two of these cards over the Black Friday/Cyber Monday sales. Card CANNOT be redeemed on a Premium Family Account. This is nowhere in the description on Best Buy's website.
From back of gift card: "This card is redeemable for full price standalone Premium subscription months purchased directly from spotify.com and cannot be redeemed for discounted or group subscriptions (more on eligibility at www.spotify.com/gift-card)."
From Spotify's website when a gift card code is not working: "Codes are not redeemable for Premium for Family or in conjunction with other discounts and promotions."