Can a bootloader modify the configure word when programming the user code into the MCU?
It depends on the specific PIC24 device, but in the case of the PIC24FJ256GB110, they can be reprogrammed.  This is because the Configuration Bits are actually implemented in volatile memory starting at 0xF80000, and copied from another set of locations called the Flash Configuration Words every time the device resets.  If your bootloader modifies these Flash Configuration Words, and then does a reset, the new values will be used by the application code.

The location of the Flash Configuration Words varies depending on the size of flash memory, but for the PIC24FJ256GB110 they are:

Configuration Word 1: 0x2ABFE
Configuration Word 2: 0x2ABFC
Configuration Word 3: 0x2ABFA


I assume these locations have to be programmed using the Table Write instructions which you are probably already using in the bootloader.

From the second reference cited below:

As mentioned before, changes to the actual device Configuration bits during run time would
cause a Configuration Mismatch Reset. This does not prevent changes to Flash Configuration
Words during normal operation. This also makes it possible for an application to change its
hardware configuration by writing new data to these Flash Configuration Words, and then
executing a RESET command, which results in reloading the new values.

References:

Section 25.0 (SPECIAL FEATURES) of the PIC24FJ256GB110 Family
Data Sheet

Section 32. High-Level Device Integration