If you're not currently refluxing the tower, it is already acting as a stripping column. You are likely losing product in the overheads but depending on where the overhead vapours go, it may not represent a lost product. There are a lot of non-refluxed deethanizers out there - each one requires an evaluation. If the deeth ovhds are recycled, it essentially acts as a self-refluxing tower.
Either analyze or estimate the deethanizer feed stream and just perform a simple simulation of each case to see the differential performance using any commercial process simulator. (Promax, ProII, Hysys, VMG, etc.)
efficency as compared to what? efficiency of what mechanical device? So what if you lose product, what is the financial impact is the concern. There are 1000's of non refluxed deethanizers (demethanizers) out there, they are called expander plants.
Did you move the feed into the old reflux line? That will give you some more stages.