The answer is yes,you can mine cryptocurrency with a Raspberry Pi.However, because the raspberry pi performs relatively poorly when calculating the hash, the power cost may outweigh the return, making it difficult to make any profit.
An exercise in counterproductivity
Cryptocurrency is "mined" by calculating complex equations on a computer. Any modern computer - even a smartphone - can be used to dig up COINS, but the hardest part is digging up enough COINS to make things valuable.
Cryptocurrency value typically works on two sliding scales; as more is mined it becomes tougher to mine more and the value increases. However, these scales aren't equal and even though the value may skyrocket, the complexity of mining them has skyrocketed more. Today, mining popular cryptocurrencies like Bitcoin on a Raspberry Pi would cost more in electricity that you would earn in profit.
In theory, you could develop new COINS that are less popular.That means it's easier to find new COINS, but it also means lower value. Should a new currency follow the trend we've seen from currencies like Bitcoin or Ethereum, The few pennies you earn every day can turn into a lot of money in the future.
Mining cryptocurrency with a Raspberry Pi can be fun, but that should be the only reason you try. It's simply not profitable.