Ultimately it depends on what you are looking for.
You could certainly cover your windows with plexi for possible added energy and sound performance, but before going to the expense and trouble I might ask if you have a particular way of attaching the plastic to the frame and if you intend to put-it-up and take-it-down like a storm window?
One consideration, the shrink film that you apply inside and then tighten with a blow dryer will have more energy advantage than a sheet of plexi loosely applied and for significant less cost.
How old are your double pane windows? Are they leaking air? Do they have condensation issues?
They are double pane Andersons that are 15 years old. No condensation. I was going to screw them into the frame as a permanent piece. Our home has no trees to isolate the big winds we have up on our mountain.
I thought by having an extra 1/4 inch of plexi it would isolate the windchill factor, and the noise during the very cold winters up here.
For sound performance an acrylic sheet (plexiglass) is about half as good at blocking sound energy as is a sheet of glass the same thickness.
If you install it by simply screwing it into the existing frame, you are going to have very little sound blocking advantage since sound will simply slip by any openings it finds. For sound blocking, in this application, you need to make the install pretty much air-tight.
Unfortunately, this will then contribute to possible condensation issues since moisture will have trouble getting out thru the no air tight window...
And, acrylic may yellow or become brittle if exposed to the UV rays of the sun...or it may not depending on whether the maunfacturer added a UV inhibitor into the product when manufactured.
As the consumer the only way you will know for certain is if the shett yellows or not with usage.
Honestly, based on what you said I think that you won't be very happy with the results that you are looking for.