I'd suggest saving your pennies and spending them on a quality Blu-ray movie
If you have a standard FHD projector (1920x1080) Yes: either the top and/or the bottom of the screen won't be illuminated, or (if you zoom the image) the sides of the image will be cut off.
If you zoom the projected widescreen image to fill the screen to its edges, there will be larger areas at top and/or bottom which are not illuminated by the projector. Some people like to cover the non-illuminated screen areas with a dark non-reflective cloth, similar to what's done in commercial movie theaters. This usually works more easily with screens which have a 2.35:1 size ratio to start with.
Unless you have a 16:10 projector (i.e. one intended primarily for use with computers instead of home theater), parts of it won't be illuminated. If you watch much 4:3 ratio source material, you would be able to zoom them to get a slightly taller image, though.
I'd suggest saving your pennies and spending them on a quality Blu-ray movie
