The current year's council tax liability is included in your income and expenditure statement as an essential outgoing, as are any catch-up payments for that year you have agreed with your local council.
Arrears for a previous year can be included. The exception to this is when bailiffs have already gained access to your home, in which case it is too late.
It is untrue what you have been told. Council tax is a debt and can be included so it you have not entered the IVA yet get a new IP otherwise speak to Creditfix and get them to include the debt.