If India didn't have a treaty signed with USSR , they would definitely have joined the war. The treaty acted as a deterrent and Russian navy positioning it's nuclear capable fleet in the waters of Indian ocean thus encircling the seventh fleet of US didnt help matters either.
With regards to Detente , it was still at the infancy and the first major breakthrough didnt come until 1972 (a year later) when the two countries signed the SALT 1 treaty.
Besides the Detente argument is weak considering it was marred by so many setbacks for instance NATO becoming nervous at the deployment of new Russian SS 20 missiles in 1979 and thus deciding to deploy its own cruise missiles in Europe to act as a deterrent to a possible Russian attack in Western Europe , American refusal to accept SALT 2 treaty and of course the Soviet invasion of Afghanistan which further fueled the tensions.