I have never been touring before, but i would very much like to try. Is it possible to do so on a MTB (with approriate tires, of course)?

If so, here is my situation:

It has to be made by Giant.

I am pro-dealing it from the lbs, so price is not much of an issue, though i would prefer that the bike retail at around 800-1000$.

Finally, what modifications should i have made on the bicycle?

Thanks in advance for your advice.

my Giant mtb tourer

If you'll be riding mostly on paved road, get a chromoly front forks. GT bikes used to come with good chromoly forks. You should be able to pick one up real cheap.

Giant do make a touring bike in the OCR range.
Plenty of people do extended touring on MTBs; provided they are not too sport-oriented, they make fine touring bikes.
You will need a model with fittings for rear rack and pssibly fenders. Disk brakes often interfere with the fitting of a luggage system.
If you are carrying a heavy load, look for heavily spoked wheels (36 rather than 32). A touring tyre is more efficient than an off-road knobbly.
On extended tours, it can be difficult to maintain suspension forks. Switching to ridgid forks with pannier fittings is a good idea, although Old Man Mountain make pannier systems for suspension bikes and many people do shorter tours on sus forks.
Flat bars are OK but you will need alt hand positions. Many people fit bar-ends but aerobars are probably more efficient.

I started to answer this with all sorts of suggestions, but came to the brick wall... do you actually have a bike right now? And if so, what is it? Why can't you go for short overnight trips on it? Why do you require a Giant?

It's impossible to answer generalised questions when it comes to touring.