It depends on better off in what sense. There is obviously benefits in using a separate amp in terms of lesser net heat accumulation inside the receiver. other than that, depending on your room dimensions, sitting distance, how loud you listen to, external amp will give you additional power if you purchase one that is more powerful than the receiver. For lowering the operating temperature, you can achieve the same by simply adding a $15 quiet Infinity fan on top of the enclosure, providing the unit more room to breathe, or both.
That Anthem amp won't give any meaningful additional output compared to the SR8012. To make some meaningful difference you will need something like the MCA525, or the MCA225 if you just want to make some gains in Stereo.
"Continuous" is not well defined in amps and receivers power output rating, other than it seems obvious that most of the time they don't not mean continuous literally. It could simply mean average power output based on a "continuous" sine wave for a minute, 2 minute, 5, 10 or 15 minute duration. You can email Marantz, but their customer service will not likely give you a credible answer, unless you can somehow talk to the guy in charge of the engineering/design department. Sometimes they tell you if they follow certain rules such as FTC, DIN, IEC's etc.
