Difference between "accelerator" and "microcontroller"?
As far as I know, the Intel D1000 (or the D2000) does not have the functionality you mentioned.

The Intel Curie, also part of the Quark series, does have a pattern-matching accelerator that allows it to recognize patterns from various incoming sensor data.  For example, you could program it to use its accelerometer to tell if a person is walking or running or has fallen, or if worn on the wrist to detect hand gestures.  The accelerator runs independent of the Curie processor itself.

I think the synthesizable reference refers to the ability of the 128 node neural network pattern matching circuitry to perform machine learning, and thus synthesize its own circuit.

The Intel Curie module is a SoC (system on chip) based on Intel Quark SE, with the processor, accelerometer, gyroscope, and BLE in one module.  It has 384K of Flash, 80K of RAM, and runs the x86 instruction set.

You can get an Arduino board with an Intel Curie (the Arduino 101) for just $30.  I am currently using the Curie module in a project.  The Arduino 101 is mostly compatible with standard Arduino I/O, including accessing the BLE, however as far as I know you can not currently access the accelerometer and the pattern matching hardware using normal Arduino programming.