This is correct, AFAIK. 
What is a person? Or rather what am ‘I’?
There are a host of options to choose from… At the broadest level I could identify with my social position (son/ parent/ employee etc) or with this body, or with perceptions, thoughts, consciousness etc.
As we drill down, rejecting all these options we narrow down to the idea that ‘I am this stream of Consciousness’. But as the Buddha points out in MN38, even that process can be dissected into 6 sub processes. ‘I’ can be seen as a construct… a clinging to impersonal experience, a conceiving based upon ignorance… like a lingering scent associated with the parts of a flower (SN22.89). In modern terms this person - ‘I’ - am a lot like Siri but with craving, attachments and defilements!
What happens if ‘I’ put aside that sense of identification to Consciousness (Nibbana)? What’s left when all the processes that have so far been considered to be ‘I’ cease too (Parinibbana)(SN12.65)?
What remains?
…### ??? Undefined ??? ###
So what am ‘I’? Do I exist? Do I not exist? Both? Neither? In the 3 times (past/present/ future)?
All these questions can now be seen as inevitably flawed - they are of the type “Where is the Hippogriff ?” 
. The best possible answer is in terms of Dependent Origination, IMO.
SN22.87
One who sees the Dhamma sees me; one who sees me sees the Dhamma.
How deep in Meditation need one go to be able to see through the sense of Self identification- the ‘I’ , ‘my’ and ‘mine’ making? I suspect that that varies, depending on the amount of insight one achieves. 
(All views are personal opinions and not reflective of any kind of ‘achievement’ on my part!)