Is Base64(SHA1(GUID)) still unique like the original GUID?
Base64 provides a 1:1 transform from input to output (and back again if desired). So if you take a set of unique items and base64 encode all of them they will all be unique.

So the question becomes if you run a GUID through SHA1, will the resulting hash have the same uniqueness as the GUID?

The answer is practically - yes; theoretically not quite. Multiple inputs to SHA1 map to the same output, but in reality if your GUIDs are unique then there is negligible probability that there will ever be a collision leading to loss of uniqueness.