I recently got myself the Arduino Mega 2560 PRO (Embed) and I am wondering if I can power this by applying regulated 5V to the 5V pin.
Not only can you power it by applying regulated 5 V to the "5V" pin, that is the only way you should power it if you intend to connect anything else to the board. And I very much suspect that you do want to connect other things to it as it is only really decorative otherwise.
As groundFungus points out and I also frequently do out of great frustration, the "onboard 5V regulator*" is present only in order to resemble the original Mega 2560 design and is essentially useless.
The oversight is not comprehending what the "Vin" or "RAW" terminal is. The regulator on the predecessors, the Arduino Duemilanove and previous, then the UNO/ Nano/ Pro Mini/ Mega2560/ Leonardo/ Pro Micro has very little heatsink, so will not pass very much current (depending on the input voltage and thus, how much voltage it has to drop) before it overheats and (hopefully reversibly) shuts down.
It is essentially a novelty provided in the very beginning of the Arduino project when "9V" power packs were common and this was a practical way to power a lone Arduino board for initial demonstration purposes. And even then it was limited because an unloaded 9 V transformer-rectifier-capacitor supply would generally provide over 12 V which the regulator could barely handle.
Nowadays, 5 V regulated switchmode packs are arguably the most readily available in the form of "Phone chargers" and switchmode "buck" regulators are cheap on eBay so these can be fed into the USB connector or 5 V pin to provide adequate power for most applications. Unfortunately, many tutorials or "instructables" are seriously outdated or misleading and have not been updated to reflect the contemporary situation.