Might, might not. Check the trunk for any rot anywhere - that'll look like soft soggy areas, possibly with white stuff oozing out, or at worst, orange gunk coming out. If there isn't any, suggest you wait (although you can remove any dead leaves). It may yet produce new growth either up the trunk, or from the base - it looks as if that's what it did last year, there's quite a bit of new growth which has been affected by the cold there. If/when it does show new growth, chop it down to wherever that is - and hope we don't have another arctic winter this year. This plant is called Cordyline australis by the way, and welcome to GoY.