Yes, you can !

Be carefull when loading software into the controller. Do not loose TOO much !! Make a functional backup of the existing bootcode.

From their datasheet CC01 ....

Programming-Interface
Several Application Program Interface (API) calls are available for use by an application
program to permit selective erasing and programming of FLASH pages. All calls are
made by functions.
All these APIs are describe in an documentation: "In-System Programing: Flash Library
for T89C51CC01".
This is available on the web site.