Hello; It so happens I am considering something like that for an old metaframe tank with a slate bottom. The last leak was thru the slate. I managed to stop it by smearing a layer of silicone over the area, but do not think this is a good long term fix. The tank is an old survivor with a stainless frame. I have been considering fitting a piece of plexiglass to the bottom but from reading posts it may be that silicone will not stick to the plexiglass very well.
Are you thinking of plastic sheeting like that of a plastic bag?? I can think of a few potential problems with this. For example, gravel and other things will likely poke holes in it over time. Also a lot of leaks are from some other part of a setup, not always at the bottom.