Yes, but observing the process is less interesting than watching paint dry. Rocks called iron-manganese crusts grow on mountains under the sea. The crusts precipitate material slowly from seawater, growing about 1 millimeter every million years. Your fingernails grow about the same amount every two weeks.
In a volcanic eruption, the violent separation of gas from lava produces a "frothy" rock called pumice, loaded with gas bubbles. Some of it can float, geologists say. I've never seen this happen, and I'm thankful for that.