Their table would be graced by pieces of aubergine the size of an index finger, fried and dusted with cumin.

是的，网友判断正确。

划线部分是名词性词组，作 pieces of aubergine 的定语。等于说：

Their table would be graced by pieces of aubergine which are the size of an index finger, fried and dusted with cumin.

the size of...作定语举例：

The British pavilion is an impressive steel and glass construction the size of Westminster Abbey. 

这座英式亭阁是令人赞叹的钢和玻璃建筑，大小和威斯敏斯特教堂相当。

《柯林斯高阶英汉双解学习词典》

It may even be possible to make computers the size of a pinhead one day. 

甚至有一天计算机都可能做成钉头那样大小。

《柯林斯高阶英汉双解学习词典》

If it were a country, California would be one with more people than Canada and an economy the size of China's. 

如果它是一个国家，那么加利福尼亚州将是一个人口超过加拿大，而经济规模与中国相当的强国。