Good question with linguistic and history.
The word and object of 葡萄 in China from Han dynasty from when B.C. 202, imported from West Region( now Xinjiang Province) and mid-Asia. Historical records noted as 蒲桃，蒲陶，蒲萄, which is obviously according to the original pronunciation.
Coincidentally, Portugal, Chinese people knew it in modern time , which is the similar pronunciation as the 葡萄.
Now you know, the answer is negative. The Chinese word for grape (葡萄) doesn't come from the name of the country Portugal. On the contrary, the translation name of the country Portugal in Chinese 葡萄牙 is from 葡萄. Because of the pronunciation.
