I haven't tried it, but I don't see why not. Sure, cucumbers have a lot of water, but you're already crushing them in a blender or processor to make the sauce, so you don't have to worry about bursting cell membranes.
I suppose if you made some kind of chunky tzatziki, you might be concerned about a change in texture. I've never seen a chunky tzatziki (and it doesn't sound very appetizing, IMO) but searching Google, I found mixed advice on this subject. Some of the recipes I found call for finely chopping or mincing the cucumbers and in that case I can see why you might have some issues.
Globalpost.com has this advice on a page called, appropriately, How to Freeze Tzatziki:
You can freeze extra tzatziki for later use, but don't expect perfect
results as you might with foods such as lemon curd. Cucumbers usually
become mushy when frozen, but the acidity in yogurt does protect some
of the original crunch. Yogurt fares better in the freezer, but some
liquid separation can occur and it might taste more acidic when
thawed. You can stir the liquid into the tzatziki sauce after it
thaws, but it might not be as smooth.
If the cucumbers become too mushy in the thawed tzatziki, you can
strain them out of the yogurt and stir in fresh cucumbers.
My advice would be, try to puree your cucumbers really finely for sauce that you intend to freeze, to minimize any change in texture.