We wouldn't know, different programs operate differnet, I'm assuming someone would have to create a entire different miner for the PS4 etc.
This would be difficult to start now, because we don't know the final details on the consoles.
It sounds like it's possible, doesn't mean it's going to be profitable.
C++ is a pretty versatile language. AFAIK almost every console runs it.
Also, the miner theoretically wouldn't have to be completely rebuilt for the ps4. If the hardware leaks are correct about the stuff basically being PC hardware, all we would need is an exploit that can bootstrap a Linux environment sufficient enough to run the code. No modification to the miner would be necessary. Such a feat has been accomplished on the ps3.
Also all of the discussion above is about the Xbox 720, since it runs Windows 8 Basic, and has just been built on top of that, it should accept almost any language with its redistributable (Leading me to think XNA Framework is going to be modified for it). Also with some hacking, we could potentially get the xbox to accept CGI executable programs and get cgminer running from the start (assuming its hardware essentially runs just like a computer). We wouldn't need to get a Linux environment emulated at all.
The only issue with these two consoles are their BIOS. The motherboard shouldn't be an issue, but the way the BIOS interacts with the hardware could potentially be different. If so, the miners would have to be modified to interact with the hardware.
Also, it wouldn't be profitable for Bitcoin, yes. Would it raise its awareness among the gamer crowd? Yes. However, we mainly are looking at its profitability for mining alt coins.