What would the consequences of this be? She seems to have helped put her son on the Ottoman throne even though he was relatively incompetent (unlike many of his predecessors).
Mustafa, his second son, would become sultan most likely. And if there is no Hurrem the odds are another Slave girl might get the attention of Suleiman. But okay, lets say Mustafa becomes Sultan in 1566, he is already 52. Not long to go.
Roxelana had different competent sons. Mehmed died to early aged 23. Suleiman loved that son the most.
Bayezid, a good fighter but not a good strategist. Was prefered by Roxelana and his sister Mihrima. But Roxelana died and so did Bayezids sole protector.
At last there was Cihangir. Physically weak but a really smart prince.