Is it a carb'ed Monster? If it's anything like the 600SS then no you wouldn't have to, but you'd need to remove the tanke and airbox to get at the carbs, which can be a real pain!
yes, if it is carbed, you will need to take the tank and box out. but you could also get away with not replacing it. I removed mine altogether. It's ugly, jams, and the choke can be pressed in manually at the side of the carbs. This way, you dont ride with the choke on (better for the engine) I have been runing a 600 this way for two years, and removed it from the 900 as soon as i got it. i recommend it.
Don't know the setup of the bars on the monster, but the engine is the same as my 600SS and you'd definitely need the airbox off to replace the other end of the choke cable on the carbs.