Can the Intel Curie modules be programmed in assembly using the Quark toolchain?
After some research, I came up with somewhat of an answer to my question.

First, Curie contains a Quark SE C1000 and not a D1000. 

The higher level toolkit takes over a huge amount of boot time setup of the processor (search for Quark), which would seem necessary when using what amounts to a CISC processor from more than 30 years ago as a MCU.

Intel System Studio is usually used with the device, which supplies a C compiler and Arduino or a RTOS called Zephyr. Normally you are limited to C, but if you use an assembler that can produce the proper type of file (ELF) it can be linked with the toolchain.

One assembler that can be used is flat assembler.