I'm curious if the ps4 is powerful enough to emulate the ps2 this time around.
It's not a matter of simply power. The support for PS2 would also need to be built into the OS (and would probably require extra circuitry and chips on the motherboard), increasing the cost.
Not really. PCSX2 can emulate many PS2 games with astonishing quality. Though it may not be suitable for "release" or "professional" quality, as there are occasional glitches here and there plus sudden major slowdowns.
The PS4 however uses GDDR5 which has terribly high latency. And PCSX2 needs very low latency because it's constantly checking for floating point operation errors (PS2 diverges vastly from IEEE 754 behavior) which could kill fully-software-based PS2 emulation solutions on the PS4