Not necessarily...but I guess you could say that generally, that might be true. But that is sort of looking at it backwards.
Look at the max aperture of the lens (F2.8 for example). A lens with a max aperture of F2.8 might need to have a large front element...but it depends on the design of the lens.
If you have two lenses, both with a max aperture of F2.8, and one has a 67mm filter and one has a 77mm filter...they both still have a max aperture of F2.8, so they should have the same light gathering ability. There may be slight variances in the image quality...but that is also a result of many other factors like the type and quality of elements within the lens etc.