Not really. Ps2 slims take 8.5v. 11.1 packs will fry them without a heavy duty regulator, and 7.4v packs wont run em. Your best bet is to find a 9v portable dvd player backup battery. These are the best ones Ive seen, but they are rather hard to find, nowadays. They are just 6 18650 lithium cells and a regulator board, but that board is much nicer than any other solution I have seen. I have confirmed you can add cells in series and build the pack up to whatever capacity you want, assuming you use identical 18650s, of course. I think I have some laying around here, I will look into it.
This man speaks the truth. If you can find one of these, they're quite awesome. It's what I used on my (now-deceased) PS2p. Also, what Ben originally used on his PS2p as well. They're great packs, and, occasionally, they'll pop up on ebay for dirt cheap.
I wouldn't try to copy MAF with anything. I always had to explain how regulators worked and taught him the difference between linear and switching. He usually sent things to me or someone else to finish or fix. The only parts he did himself was the casework.
No. Just no. Firstly, it wouldnt be enough voltage. Secondly you would go through batteries REALLY fast. Like, a new set every 15 to 20 minutes of playtime.
And whats with the trend of people wanting to use standard alkalines all the sudden?