It won't have inflation caused by the underling supply being increased which is the largest component of inflation. But you’re correct to point out that inflation has other causes (eg. natural fluctuations in demand for goods and services) that will still exist in FixedSupplyCoin world.
The government will always require taxes and utilities to be paid in their currency. So, every one will need to sell cryptos to fulfill those electricity bills and taxes. This sell pressure will carry on a inflation into cryptos.