Yes it matters. Since screwdrivers (or variants of them) are pretty much all I drink I can say that cheap stuff can give you a very nasty aftertaste. Lots of times it can be covered up if you add some other juices or flavors. Pineapple usually does a good job of killing it (not much just a bit) or sometimes grenadine for that sunrise effect. Then again I've never had really good vodka either, only mid grade stuff.
The oj also matters. I tend to have sunnyd cus thats what my roomate has for breakfast, but different juice will make a difference.