Yes, mining doesn't use the memory on the card at all. Most people under-clock the memory all the way down to save on heat and power consumption. I believe the lowest you can go on the 5830 is 300MHz, but don't quote me on that.
If I push my 5830's below 300MHz memory clock, I lose mining performance.
At 300MHz and above, I do not lose any performance.
So you *can*, but there's no point in lowering further.