I would think that you could. But as of june 30th, seems to be too late in zone 6. In order to get a head start in zone 6, you should have started your seeds indoor, in May and have transplanted to garden after night temps reached over 50F.
Eggplants need a long and HOT growing season to grow and fruit, much more so than tomatoes and peppers.

In zone 8 GA, I direct sowed my Japanes eggplant seeds in the garden, back in mid April. It took about a month to germinate, because it was not warm enough then. Then they germinated but grew very slowly until night temps got over 50F. Now they are very strong, about 2 ft tall and flowering.