Of course it is possible! What an absurd question, considering the word cheap isn't objective...
Anyway, today me and my cousin had a debate on whether or not an okay foreign tour (starting from DEL) is possible in under INR 20,000. I was vehement that it is indeed possible, whereas my cousin asserted that INR 20,000 is too low for an acceptable foreign tour. The underlying question was whether or not making an ultra-cheap foreign tour (in under INR 20,000 per person), assuming it's even possible, makes more sense than spending a similar or slightly less amount to visit a place within India.
I've visited three foreign countries till date. And my experience strongly suggests to me that there should be at least a few foreign destinations which can be had from Delhi for under INR 20,000 per person. I spent a few minutes on Cleartrip to check ticket prices of flights from DEL to various foreign destinations nearby, and I'm largely convinced that acceptable tours (of two nights and three days duration) under INR 20,000 should be easily possible.
Specifically, return tickets from DEL to Kathmandu, Kuala Lumpur, Colombo, Muscat, Kuwait and Dubai are priced reasonably (click here for screenshots of prices seen on Cleartrip), and a bit of frugality should allow one to have an acceptable overall experience, while spending less than INR 20,000 per person (the per person cost is even more achievable if more people are added to the group).