Probably not - if the palm is a Cordyline australis, and its shooting from part way up the trunk, no. If the shoots are coming up from the base, if you can get some good root with them, then possibly. Usually, though, the shoots arise directly from the trunk, even at the base, so getting roots isn't possible - unless the main trunk has died and you dig it up and chop it in such a way that you do get some root with the plantlets at the bottom.