Not by default, no - and note that Alienware systems are not sold as widely as Dell systems, so there is no support for these in many locations.

Two dell representatives from us and Canada said that they do have international warranty and I particularly asked them that new 15 model ain't available in India. Is it covered? They said yes. Whom to believe? You or them?

If I were you I would think this.  If they don't sell the Alienware in your country or that particular model, I wouldn't trust the Dell Reps as it is possible they misread the information. I skimmed the Dell Consumer Warranty document and I didn't see anything that stated it was international.