Can a bitcoin bank solve the problem of intensive value fluctuation caused by hoarding? Let's assume a bank dealing in bitcoins is not any central of government bank that could control the money supply. 

Instead, let's say there was a bank where the people would deposit money at some interest rate, and also the bank would give loans to the people at some interest rate.

The intention of the bank would be to keep the bitcoins in the circulation (by taking and giving benefits to the people with some interest rate) instead of hoarding, as we know hoarding may hurt the Bitcoin economy.

Or, suppose I deposit some BTC in HSBC bank (or some kind of reliable online bank), and HSBC will give the interest every month.
Saying people are hoarding bitcoins is out of focus: they are simply "not spending them" because there aren't enough ways to spend them.

Allowing loans wouldn't improve the situation, since there still wouldn't be many ways to spend those loaned bitcoins.

Finally, bitcoins already are a currency subject to deflation, and they are also (more or less) constantly gaining value against traditional currencies, so just holding them increases their value.

To sum it up, not a terribly good idea, and definitely not ground-breaking.