This should demonstrate that Curl does parse literal slashes in the username and password fields:

$ http_proxy=http://user/name:pass/word@localhost:22 curl -v http://example.net/
*   Trying ::1...
* Connected to localhost (::1) port 22 (#0)
* Proxy auth using Basic with user 'user/name'
> GET http://example.net/ HTTP/1.1
> Proxy-Authorization: Basic dXNlci9uYW1lOnBhc3Mvd29yZA==
> User-Agent: curl/7.40.0
> Host: example.net
> Accept: */*
> Connection: TE
> TE: gzip
> Proxy-Connection: Keep-Alive
> 
SSH-2.0-OpenSSH_6.2
Protocol mismatch.
* Recv failure: Connection reset by peer
* Closing connection 0
curl: (56) Recv failure: Connection reset by peer
[Exit 56]
$ base64 -d <<< dXNlci9uYW1lOnBhc3Mvd29yZA==
user/name:pass/word$