Wow, somehow never thought that the device is named after the fruit. Their names can be even closer in other languages, f.e. in Russian they are nearly the same word, just different genders.
No. "Pomegranate" comes from the Latin "pomum granatum," the 'fruit having many seeds.' Granum means grain or seed, and granatus is a pseudo-participial form (like "mentulatus") meaning 'endowed with seeds.' Granada, the city, likely derives its name from Arabic.