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Yes, but you need to get rid of as much of the moisture as possible after you grate it, so be ready to go through a lot of towels. The easiest way to freeze grated zucchini for future use is to put a measured amount (1 or 2 cups, depending on what you want to use it for) into freezer bags.
Or you can cheat and grate and freeze as is. Due to the high water content of zucchini, the cell walls will burst when you thaw it. Super, super easy to just drain that off and then use the remaining grated stuff. Either way (patting dry before freezing; letting the freezing process do the work for you) the result will not have nearly as much moisture as fresh -- more flavor/less moisture. You may need to adjust your batter to accomodate.
Or maybe make a few extra loaves of zucchini bread now and freeze them? Zucchini pickles or chow chow? I've never been thrilled with frozen zucchini but maybe I didn't prepare it correctly.