seeing the legendary dogs once would be unfair to not be able to catch them, for you'd be totally unprepared. after you see it, it is not gone forever, it simply changes which route it hangs out in. for Ajox question, you simply pokedex raikou and find out the route he is currently on. be warned though, they change route every time you change route, city, etc.
i saw Suicune for the first time on route 2 training my eevee. i caught him the next day on the bus going to school.
something else good for catching them is having a wobuffet. keep it from running away and you can weaken it with mirror coat and counter. then just use hyper potions or something when his hp gets too low, then start throwing ultra balls. or, you can always use the master ball, if you didn't use it on mewtwo yet. also, they don't roar you, they run away, just like on emerald or sapphire in your first battle if you don't attack the poocheyena and it's about to knock you out, it will run away. (dumb dog.)
anyway, you can chase them for ages, and they'll be there until you catch them.