Sort of. The organization ICE didn't exist. The functions of ICE were executed by other organizations in the government and (correct me if I'm wrong) no additional responsibilities were really added to ICE whole-cloth; it's more of a post-9/11 consolidation of resources.

Abolishing ICE without considering the need for those responsibilities and what org, if any, should take them on is certainly risky. But technically, yes, we could abolish ICE and route things ICE does (immigration management, customs enforcement, non-military border security) to other executive departments (not necessarily back to their originating department, since instituting ICE also abolished some of its predecessor departments).