Is it safe to pass raw base64 encoded strings via GET parameters?
No, you would need to url-encode it, since base64 strings can contain the "+", "=" and "/" characters which could alter the meaning of your data - look like a sub-folder.
Valid base64 characters are below.
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=