Generally no. Compression algorithms search for repetitive data and replace it with a shorter code and keep a dictionary with all codes. Compressing text works excellent because in longer texts a lot of words repeat.
With video this work has been done most of the time already. Usually the encoder is performing a similar operation: looking for repeating patterns and replacing them with a shorter code. Most video files you see are already compressed, most repetitive patterns already encoded and therefore any further compression won't do much.
Sometimes re-encoding videos with a much newer encoder saves a lot of space, but this process is always a bit lossy and requires more work.
You could check if the files have any additional unwanted audio tracks and remove them, like tracks in languages you don't speak anyway.