While they were treated as Princely States for official ceremonies (i.e. during King George V's visit to India in 1911) and diplomatic purposes, Nepal, Ceylon, and Bhutan were not Princely States. More importantly, they were not considered parts of India in the terms that Indian nationalists and irredentists (like Gandhi or the RSS) wanted to keep them as a part of a united, independent India.

So no. They were not extended the option (nevermind the fact that none of the three had a significant Muslim population, the basis for joining Pakistan) and they were assumed to be Independent, with Britain's agreements with Bhutan and Nepal inherited by the Government of India, and with Ceylon's relationship with Britain independent of Britain's relationship with India.