Yes, charging a Li-Ion cell at constant voltage without ever terminating the charge will likely destroy the cell.
What will happen is that your battery will get (maybe slowly) to 4.0 V, and, if the voltage stays, the charging current will gradually decrease, and will decrease to zero. This will put the cell into overcharged state, even if the voltage was not at maximum for the cell's capacity.
Most common rationalization of overcharging process is that “the lithium builds up faster than it can dissipate. The result is that metallic lithium plates up on the anode. At the same time, the cathode becomes an oxidizing agent and loses stability”.
In other words, if the cell is subjected to CV and the current stops over time as it normally goes, ions of Lithium started to build up without the current forcing them to move. That's why the charging process must be stopped at some point. So it is not the voltage level (although overvoltage causes other bad effects), but the fact that current eventially stops, and Lithium build-up starts.
As result of electrolyte decomposition some gassing might occur resulting in bulged/bloated/swollen cell, and the cell typically looses 50-70% nominal capacity due to some irreversible changes in microstucture of electrode materials.
Bottom line - don't charge Li-Ion cells continuously.
For more scientific explanation, see this article in "Frontiers in Energy Research"