yourname.uni.cc is a subdomain of uni.cc, so that couldn't be used for cobranded hosting.
If you mean a top level domain registered at sitelutions.com, yes, as it will be the same as any other domain. If you mean their domain or subdomain redirection service, no.
In other words, you'd need to fork out the $8.95 a year.
As we've already said, you need a top level domain (which is what you originally asked).