I don't like this question, simply because there are too many variables. "CAN it be detrimental?" Well...
Windows come in single, double and triple pane; made from glass or plastic; have different insulation systems between panes, have different natural coatings and compositions for various properties such as UV protection or reflection; and many other variables. Over time glass windows will flow and warp, where plastic windows will oxidize.
Stick-on Window Coverings come in various materials (plastics usually, but that's a wide range of chemical structures with subtly different properties); use different adhesion methods such as static or chemical bond; have different coatings and compositions to create various properties such as coloring, refraction, UV protection or reflections; and again many other variables. Coatings will chemically change over time.
Light from either side of the window can have different compositions, although usually the concern is natural sunlight. Sunlight comes from different angles with different amounts of atmospheric interference through the day and year. This is why it wasn't expected that UV glass can melt siding.
So again, CAN it be damaging? Sure, anything is possible.
WILL it be damaging? We really can't say until you install it. But a bit of very light Googling didn't find any actual reports. It looks more like an attempt to pass responsibility between window and coating manufacturers. I'd say check with your window manufacturer, and follow their recommendations. Ultimately, that's the expensive repair if something goes wrong.
Remove ALL the mortar throughout.
Fill gap with Great Stuff / expanding spray foam.
Let cure and then cut off square.
Drywall the face of the sill plate to cover the foam for fire safety.
Best Answer
Reducing convection is a minor concern. The benefit described in that answer is trivial compared to the benefit of sealing against airflow through leaky windows. As a proportion of total heat loss, convection is very small as compared to drafts.
There would be a benefit to adding a second layer, but not primarily due to convection restriction.
A second layer of film adds insulation on its own. I wouldn't clutter your view with bubble wrap, which provides relatively little additional benefit. Because the seal between the first and second layer of film is (presumably) better than the seal between the inner layer and the outside world (due to a leaky window), the net benefit of a second layer is already better than the benefit from just the first layer.
All that said, the savings afforded by a second layer may not outweigh the cost of the product. My advice (having owned older homes in Minnesota) is to do a good job of installing one layer and be happy.