Mindstream considered in that fashion is a myth.
Mindstream may also reference the ability of a awareness when presented with object to become aware of object. Due to the nature of our (sentient beings) consciousness we have habitual aspect and retention. Suchly due to such fact a internal object may become a object of which awareness becomes aware and thusly elicited.
So strictly speaking yes that is correct. Functionally speaking awareness presents always in our consideration as a mindstream and continuation. When presented in result as sentient being it presents always in reference to a other moment of consciousness so thusly it is perceived always as a continum.
STrictly speaking it is not. NO object...no aware response. But to make the former statement is like saying karma is all intended....a bit misleading.
To elaborate a bit....I will not rebirth. When a circumstance exists which necessitates a aware response that approximates a similiarity to what I have previously considered to be my consciousness to exist...it will exist. It has not existed prior to that circumstance. But when it is then elicited by circumstance it comes to whit with retentive aspect and habitual formation which present the appearence of a continum. So for that consciousness a continum appears present..
It is a ignorant aspect of awareness displayed but we cannot deny its existance in a ignorant aspect of awareness so elicited.
I hope that makes sense to you but I see no logical fault in it. None can be found to my study and consideration. I can elaborate.