No.
The one in KH1 only appears in KH FM. There also appears another hooded character in KH CoM, but it's not the same one.

If you really want to fight him though, then you can buy the game online.

I wouldn't really recommend it though because other than a few little add-ons like a couple of new keyblades, a few new heartless, and a couple of more things; there isn't really much more on it other than that Hooded Figure battle.

However, if you really want to play it you can buy it on a site like PlayAsia.com. You're gonna need to buy a SwapMagic for your PS2 to be able to play it though, since it will only play normally on a Japanese PS2.

Hope this helps.

The "Hooded Xemnas" you are referring to appears only in the final mix version of KH1. And, yes he is the guy in the clip if you are speaking of the clip that appears if you leave the game on the main menu for a couple of minutes, the reminesence of KH1, as it were.

A hooded figure indeed speaks with Riku in Hollow Bastion, confirmed in Kingdom Hearts NA release. The figure is wearing a brown hooded cloak. The cloak is later thrown off to reveal a silver-haired man who identifies himself as "Ansem, seeker of darkness." No one named as Xemnas appears in Kingdom Hearts. (No, not the hooded person you mean, but bear with me a sec.)

The cloaked figure in the Final Mix is identifed as "the Unknown", as is the cloaked figure on the crossroads at the start of KH Re:Chain of Memories. And in the latter case, "the Unknown" is definitely not Xemnas.

With that said and those confusing points clarified, the opening-credits sequence of KH-ReCOM (PS2, NA) indeed includes a clip from KH-FM, showing a figure wearing a black hooded cloak.