No, they are stuck in samsara because of clinging; the annihilationist overreaches with their view because they think the problem is with “my” khandhas, which is why they hope for annihilation. But in fact the problem is with ongoing _upadana-_khandhas, and so removal of clinging is the goal, not removal of the aggregates.
When it comes to rebirth, I think there was no reason to even mention it to annihilationists; this thread goes over this facet of the topic a bit.
And, without going crazy with it, we can notice in the Kalama Sutta that a noble disciple can win these two assurances:
The first assurance he has won is this: ‘If there is another world, and if there is the fruit and result of good and bad deeds, it is possible that with the breakup of the body, after death, I will be reborn in a good destination, in a heavenly world.’
The second assurance he has won is this: ‘If there is no other world, and there is no fruit and result of good and bad deeds, still right here, in this very life, I maintain myself in happiness, without enmity and ill will, free of trouble.
Here, a noble disciple is both noble as well as uncertain about ‘another world’. SN 12.70 says the same thing.
With respect to anatta & emptiness teachings, these are facts which assist with the cessation of craving for sensuality, for existence, and for nonexistence. Cessation of the khandhas is a side-effect, and probably the reason why the Buddha was often confused for an annihilationist, especially by the numerous eternalists.
Cessation of dukkha by way of the cessation of craving: THIS is the goal.