Can I burn my Arduino Code into this:
or something similar by just using just the Arduino ISP?
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Also, to run actual Arduino code on it, you'll most likely have to port the Arduino library, if this hasn't been done before.
You may opt for something as easy as a teensy 3.2, they probably meet your requirements and work well in combination with Arduino. Or fetch one of the newer Arduino models that have comparable microcontrollers
If you still want an M3 (without development board?) you'll be entering a somewhat advanced usecase, in which you probably don't even want to rely on or use Arduino. There are far better IDE's.
I don't know about that chip I think this one also can be done as some of the other chips can be programmed using the Arduino ISP I think it can be even done for this one. This one uses an AVR ISP Programmer while we are using the Arduino one but as they have similar working It is maybe possible. For example this one