You Can. When you knock out a Pokemon, the Pokemon has fainted and cannot be captured Until you re beat the pokemon league. In the case of one time showing Pokemon (legendaries just like Rayquaza), if you knock it out, you can capture it without restarting the game and going all the way back to the point to capture it. I personally always save the game before I ever battle a legendary Pokemon, and if i successfully capture the Pokemon, i save the game right after i get it to avoid an accidental loss of data.
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Rayquaza isn't in Crystal.
You cannot catch rayquaza in fire red you must trade from either ruby or sapphire.
"Where do you catch rayquaza in Pokemon emerald?"You catch rayquaza at Sky Pillar, which is on route 131, near Pacifidlog Town, in Pokemon emerald.In sky pillar in route 131. When you make the top of the sky pillar, you will see rayquaza sleeping. as soon you press A near rayquaza, it 'll wake up and battle you! i caught a rayquaza with a master ball!
How do you catch rayquaza in Pokemon black and white
actually you can catch him i don't know how but you can search for it on youtube