Can distillation process be carried out without plates? If Yes then how? If no then why?

 Yes distillation can be carried without plates. It can be carried with packings. The whole tower is filled with various types of packing material like raschig rings, berl saddles,etc.

These impart good vapor-liquid contact when a particular type is placed together in numbers, without causing excessive pressure-drop across a packed section.

Packed columns are called continuous-contact columns while tray columns are called staged-contact columns because of the manner in which vapor and liquid are contacted.

distillation with high volatile mixture can be done by without using trays. but we have to installed grids beds inside tower and give mixture some temperature for separate them.

Distillation with or out plates, will be depend upon the mixture treated. 

Mixture with boiling point diff.100 or more can be done by simple distillation.

The use of plates or try is provide higher heat transfer area.

yes it can be done using packing on the place of trays