Apparently you can, and if you follow this link you will find a group of ham/experimenters doing just that in front of an audience.
Operating as mobile amateur radio station PA7RB (Netherlands), they were able to make contacts through out Europe on 20 meters getting good signal reports.
The system uses a coil that is placed around the trunk of a tree and then tuned using a standard antenna tuner.
The Dutch group are not the only ones who have experimented with this type of antenna.
Here is an article from the July 14 1919 edition of Scientific America on the George O. Squier Tree Antenna, named after its inventor, who was at that time a General in the US Army in the signal corps.
Before WWI there had been experiments using trees as grounds, particularly in dry areas where conventional grounds would not work well. Due to the fact that tree roots went deep into the ground where moisture was found they provided a working alternative.
Squier undertook to see if a tree could be used as an antenna as well, which would be strategically important where putting up a wire antenna being impractical. He employed the use of trees during WWI with enough success that the practice was carried over after the war.
The Scientific American article reports that the use of trees as antennas had proven to be successful, particularly with modern equipment using tube amplifiers. It was demonstrated that it was possible to receive and send radio telegraph transmissions using this method.
It was also noted that the wire connected to the tree was not acting as the antenna because it was too short for the wavelength being used.
Here is an experiment undertaken by Ralph W5JVG for a tree antenna designed to work on the 600 meter band, showing all the steps involved in building the coil and antenna tuner. The article also has a number of links to historical and contemporary articles on the antenna, including the original patent granted to George Squier.