Welcome! For dishcloths it wouldn't really matter the size of your needles. You might use fewer stitches than called for or it might end up big enough to be a towel! For socks though you will definitely want to use smaller needles (according to the gauge). Whenever you make something that has to fit your body or be a particular size you really need to use the right size needles.
OTN: Mystic Water KAL
Felted Entrelac Tote
Finished: Socks for DS
On Deck: Beret from Gathering of Lace