A long time ago I was at a bar in Nuremberg. It was my first time in Germany and my first real experience with genuine German beer. Each bottle had floaties in it, too. The bartender went through a fairly complicated process of rolling each bottle in his hands and on the bar before serving us. I was told that this was the process for settling the yeast on the bottom of the bottle before pouring it into the glass.
So in answer to your question, yes, it is safe. Older, more traditional techniques for brewing do result in residual yeast and other ingredients remaining in the bottle.
I'm glad it all worked out for you.