You really should take note of what your alternator and battery can put out, because in the world of electrics, you dont get something for nothing - it's not magic, no matter how indistinguishable from it this sufficiently advanced technology may appear. The supply has to be there for you to take it - like i said before, it's likely your inverter will draw far more power, and for a lot longer, than the lighter ever would. 600W is quite a lot of power in terms of 12v electrics - comparable to a slightly wimpy starter motor, the output available at idle, or yourself cycling up a steep hill in a slightly too high gear. It's 50 amps, which is a hell of a lot of current.
Besides its not just the alternator but the polo batteries aren't really that hardcore (and in some cases as we've seen before on UKP, the wiring..). They're not designed to take a lot of a beating, because in normal use, they don't get one.... they'll be starting the engine (750w for a few seconds maybe 5 times a day), running the ignition and fuel pumps (?? not many watts..), radio (maybe 50w) and powering the lights (5w each for side and tail-lamps, max of 60w each for indicators / headlights / brakelights / fogs, say maybe 50% of the time). Plus apart from the starter all those drains usually only occur when the engine's on.
before you know it...... snowdon!
Well, OK, the foot of snowdon, and when you find it, you'll be in the town of Llanberis. But as a nonspecific example, it stands.
What i thought was when you plug an inverter into the lighter socket/battery, it drains only what the typical lighter would drain right?
nope, sorry

anyway, as above, how long does the lighter run for? unless you have five people smoking a lot of ciggies and none of them have any knowledge on chaining them, it's not going to be anywhere near as continuous as the inverter's demand.
Anyway, the whole purpose of the inverter is to convert the 12v dc electricity from the battery to 240v ac so that the house plugs can be replicated in the car right?
Yep, that's entirely true... but again - no free rides. Due to transformer losses (inductive heating and the like), etc, the car has to provide more power than you're actually using. In addition it needs to convert DC to AC, the circuitry for which will provide further drain. And as Power = Volts x Amps, as your voltage has dropped by 20 but the power demand remains the same, the current has to increase in kind..... which leads to even further losses because the resistance of the wiring is comparitively larger to a low-voltage, high current system than a high voltage low current one.
Hope that hasnt fried your brain but im still hot on basic electronic theory, from now until about six hours after the exam.
PS the inverter replicates house plugs but bear in mind that even house plugs have a certain limit on how much drain you can pull through them (typically 13A is the maximum legal fuse value - or a little over 3kW - per socket, and about 30A for the entire house). The limits on the inverter are typically MUCH lower.
And also, your laptop's plug is just going to convert the AC back to DC again! Further losses there. If there's any way you can find to get hold of a circuit that does a direct DC-DC conversion (particularly, if your laptop takes 12V or less), as seen in all those in-car DVD and console rigs, then go for that instead.