The answer is yes.
Watermelons are a good example.
If a watermelon is large and very round on the ends, it should be well pollinated. When the watermelon is cut, the seeds tell the story. The black seeds are pollinated, the white seeds are not. The higher the number of pollinated seeds, the sweeter the watermelon will be. It takes pollinated seeds to produce the hormones that cause the watermelon to ripen.