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

Yes, you can.

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

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

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