I personally would say no. I my opinion the smallest tank you should consider a betta for is 5gallons. A small filter and heater are also neccessary. Heres an article I wrote about setting up your betta tank. http://www.aquatic-hobbyist.com/fishbertspage/homes.html
Bettas are excellent and beautiful fish and are currently competeing against goldfishg for the most abused fish in this hobby. The fact is bettas can survive in the tank you are suggesting, but I prefer my fish to THRIVE no merly survive.
Hope this helps.