정신없이 is the adverb form of 정신없다. 정신없다 has many meanings depending upon context to be busy to the point of confusion to be scatterbrained because something is exciting, confusing, hectic to be hyper to be in a frenzy to do something without control, with wild abandon It really depends upon the context. The term is used often. People even feign to be so busy!

정신없이 means "without control, with wild abandon"