Elektra
Professional
To first answer the OP's original question...in the hypothetical world where such an offer was possible, there's absolutely no chance of Djokovic giving up Slams for popularity...and certainly not 5 of them.
No secret that Djokovic in the main hasn't achieved the popularity enjoyed by both Federer and Nadal and this is due to many many factors, ...most of which have nothing to do directly with him as personally I think he comes across as an incredibly open and likeable kind of guy.
Federer and Nadal's popularity skyrocketed on the back of their success but perhaps more importantly their rivalry, something Nike were able to cleverly exploit and commercialise. Djokovic hasn't had the advantage of being tied to the mega marketing machine which is Nike and I feel that has certainly impacted his popularity when compared to Federer and Nadal.
In addition his success has largely come at the expense of 2 of the most loved and popular tennis players ever, something which hardly endears you to the fans. While I think people are now starting to warm to him as he begins chasing records he was initially seen by most as the villain and the man who prevented Federer and Nadal from creating even more history and extending their rivalry in Grand Slam Finals.
Funnily Djokovic is extremely popular throughout Asia and my thoughts as to why this might be is because it's really only been in the last 5-6 years that the ATP has started it's significant push into Asia - of course the WTF were held there prior to this but that was largely done as a means to ensure Asia got to experience the top players, a key component of their marketing strategy. In the time tennis has exploded in Asia, Djokovic has largely been the top dog and therefore their go to guy...something I'm sure would have influenced UnIqlo's attraction to him.
Tennis is borderline nationalistic, the country you hail from can impact your markeability and appeal. Monica Seles is from Yugolslavia but she is adopted child of the United States and most of her success is caused she lives in the US. Maria Sharapova is from Russia but she does not act Russian she acts more American and lives in America. That impacts her popularity and marketability around the world. Switzerland is a neutral country that does not have any wars, quiet country and a money haven for the rich. So you have people that will be drawn to Federer cause he hails from Switzerland.
Spain is a romantic country, exotic and often free spirited. You have Rafael Nadal who embodies that romanticism of the Spanish Cassanova.
Then you have Andy Murray who comes from a country that has pride in themselves and has strong ties to British monarch. Andy Murray is not the greatest looking guy but his appeal will be bigger cause of the country he hails from.
Djokovic hails from a country often misunderstood, has close ties to Russia and a Slavic nation. Most Slavic people are looked upon as "others" in that European hiearchy.
Most of Djokovic's appeal has been in Asia, his major sponsors are Asian companies. Now that Kei is in the mix, Asians would go for Kei over Novak.