As the old adage goes, size DOES matter. If you use larger needles than the size recommended (assuming you'd normally knit to gauge) you'd get a more open, loose knit because you'd have fewer stitches per inch. Patterns would require you to recalculate the number of stitches to cast on, and the amount of yarn needed to do a project might change, too.
That's why gauge samples are so important. You use the size needle needed to get the number of stitches per inch that your pattern requires.
Hop this helps!