You probably would not blow the speakers but you will damage it.
In most cases if you turn up your volume past 3/4 of the way, your sound will get distorted. SPL (Sound Pressure Level) is measured based Decibels (db) per Watt at 1 meter. Loudness has to do the number of db and the distance from the which you're listening. However, for every doubling of the distance, you'll lose -dB and for ever doubling of the amplification, you'll gain +3 db. This means that when sitting in your car, you'd be listening to your speakers at approximately 1-2 Meters from the speaker. So you might lose anywhere from 0-6 db's. and for ever doubling of the wattage (amplification) you'll gain +3 db. So if you start with a 90 db speaker you'll be at 84 db to start and then you amplify by lets say 60 watts, and you'll be at 102 db where as 120W will give you only dB. So you should start with speakers that already have a high SPL.
Based on the above calculations, you don't need a 200W speaker. You should look for speakers that have low wattage, but high SPL. You need to start with something that is already at 92+ db. Just to give you an idea, a hairdryer has about 80 db, lawn mower has 90db, and Car horn 110 db, where a rock concert will have 120 db.
If you want louder sound, you need to upgrade your speakers and your Amps. You may do this using the factory head unit. You'll need get Speaker to Line-in converters for the wires that go to your doors. then, rewire each one to each channel of an amplifier, then run wires back to speakers.
Most amplifires now have gain control that will make your speaker louder where the bose system will not have that.