Could this simple circuit charge li-ions in parallel?
Lithium batteries are dangerous.  If you look at the application circuits on the datasheets for Li charge controllers (Linear Technology, Maxim, etc.), their complexity is a direct indication of this.  Incorrect charging current can cause the batteries to burst, burst into flame, or both.
There is nothing to assure that the charging current is distributed evenly among the cells.  If your idea is that as each cell reaches 4.2 V, it stops drawing current so the 500 mA is available to the other cells, know that lithium chemistry does not behave that way
The charge scheme you describe is common for lead-acid chargers, with a very simple transition from main to float or trickle charging.  Note that those chargers usually do not have a temperature sensor strapped to the side of the battery, whereas in Li systems this is very common.  I recently rebuilt a Dustbuster-style hand vacuum.  Five Li cells in two groups, 2 and 3 batteries.  Each group has its own thermistor, and battery management is handled by a PIC microcontroller.