This question is over 4 years old, but since I somehow ended up here from Google I think I'll answer it for posterity.
"MATLAB Coder™, Simulink Coder™, and Embedded Coder® generate ANSI/ISO C/C++ code that can be compiled and executed on any DSP or Microcontrollers"
So yes you can code the system because it's just C code, but regarding the TI C6000 series there are no specific optimizations provided by Mathworks:
"With the exception of C2000, MathWorks does not offer an Embedded Coder Hardware Support Package for the devices listed on this page. However, you can use Embedded Coder to customize the generated code for TI processors using published APIs and reference examples. For example, you can generate processor-specific (non- ANSI) optimized code and perform processor-in-the-loop (PIL) testing with execution profiling. Third Party Connection hardware and software products may exist, and MathWorks Consulting Services is available to aid with hardware integrations."
So check with TI to see if they have a plugin for their target processors.
Quotes taken from here: https://www.mathworks.com/hardware-support/texas-instruments.html
And no, you don't need "continuous communication between processor and MATLAB" unless you're doing "processor-in-the-loop" (PIL) testing, which is a nice feature.
