Is the 3' panel solid wood with vertical grain? If so, no, you shouldn't glue it and you do need to allow for movement. If the panel is plywood, go ahead and glue it. If the legs and the table top are both solid wood of same species and going in the same direction, you could actually glue those if you wanted too and you don't have to allow for movement since they would move together.
I do not prize the word "cheap." It is not a badge of honor...it is a symbol of despair. Cheap prices make for cheap goods; cheap goods make for cheap men; and cheap men make for a cheap country. ~ William McKinley