Nope. Your father may have been thinking of Chinese sticky rice mortar - which, as the name suggests, consisted of sticky rice soup mixed with lime. (It worked much better than you might think)

Roman concrete (like modern concrete) was a mixture of water, sand, lime, and an aggregate (bits of stone or ceramic). The Romans did experiment with their aggregates, using lighter or heavier materials as required by the function of the concrete structure (for more detail on that, I refer you to my video on the Pantheon). But to the best of my knowledge, they never used organic materials. In general, Roman architects (who were not formally trained, and learned their trade by rote) were quite cautious in their engineering, and especially in their use of materials.