The answer, I’m sorry to say, is yes.
The long standing rule is that employees have “common law” notice rights in addition to their ESC termination rights upon without cause termination UNLESS the contract specifically and unambiguously limits them to ESC rights. That’s why many employers insert contract clauses specifically saying that employees have no other rights for without cause termination except those provided under the [in your case] Alberta ESC. Over the years, there’s been a lot of litigation on whether these clauses are enforceable, with court seizing on even the slightest of ambiguities to rule in the employee’s favour.
HRI reports on these cases regularly and I believe even listed a case or 2 from Alberta as among our Top 10 HR Cases of 2018. Hope this helps.