Is there a significant benefit to using plastic window insulation year round?
If the plastic reduces air exchange between your home and the outside world in the wintertime, it will do the same thing for you in the summertime. You will get some benefit from the plastic in the summertime. I can't tell you how large of a benefit. But, based on my own experience, the tape that holds the plastic in place tends to grow loose after a season or two, so the quality of seal will deteriorate and you may find yourself having to put new plastic up anyway to maintain the seal. 

Also, in my home (1921 with single pane windows) the impact of the plastic could not really be measured in terms of utility bills. It was nowhere near 50%. You will probably find that it makes the room much more comfortable, though.