No, in your situation it is not possible. Mostly, only three types of accounts are available to individuals:
- Savings ( Resident): You need to be in India to get this account. For identification, either only passport (Indian passport; or foreign passport with Indian work visa) is required, or few other types of address and identity proofs are must. Maybe a foreigner living in India can get this, as anybody who lives in India for minimum 182 days in a financial year, is Indian resident for tax purposes. Obviously the ones on tourist visa can not stay that long, unless they are of Indian origin.
- NRE (Non Resident). Any Indian citizen who is NOT in India for minimum 182 days in a year, is eligible to open this account. If he moves out, he is supposed to convert resident account to this or NRO. Money can come in only from outside India. You can spend this money freely in India. As of today there is no tax, and you can take the money out of India without any issues.
- NRO (Non Resident) same as above, except money can only come from inside India, there is a 30% tax, and upper ceiling for repatriation of money.
So, a complete foreigner can open account in India, only if he is working in India, a type of Savings account, and that account too will be linked to his resident status. If he leaves work, he needs to close this account.
Edit: There are business accounts, and current accounts, but those are available only to businesses. Further read at SBI gives a good snapshot