Can I select my country as India, but have USD as the base currency?

Yes, you can.

In order to create an Organization with India as Country and Base Currency as USD,

• Create an organization with some other country name (say Singapore) and choose the currency as USD.
• Once the organization has been created, click on the Gear icon, select Organization Profile and edit the country name as India and finally click Save.

Note: This case can be applicable for all the organizations having their country as USA, UK, Canada and India wherein the user wishes to choose a country but have a different base currency.