This question is explicitly posed, and left unanswered, in the new agreed statement from the Anglican-Roman Catholic International Commission titled Mary: Grace and Hope in Christ.
The two doctrines are in question. The doctrine of the Immaculate Conception states “that the most blessed Virgin Mary was, from the first moment of her conception, by a singular grace and privilege of almighty God and in view of the merits of Christ Jesus the Savior of the human race, preserved immune from all stain of original sin.” The doctrine of the Assumption says, “The Immaculate Mother of God, the ever-Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory.”
Since the first doctrine was defined by Pope Piux IX in 1854 and the second by Pope Pius XII in 1950, Anglicans have questioned whether these doctrines must be held by believers as a matter of faith in view of the fact that the bishop of Rome defined these doctrines independent of a council of the church. Indeed, we have asked whether it would be a condition of the future restoration of full communion that we be required to accept these definitions. Whatever the merits of these doctrines in “understanding Mary as the fullest human example of the life of grace … and [joining] with her as one indeed not dead, but alive in Christ” (Paragraph 65, Mary) my answer would be, "No."
There are many mysteries of the Christian faith quite beyond our ability to understand or articulate easily. Among the most basic of these would be questions as to the very nature and internal life of God. Attempts to frame these mysteries so that people could “get their arms around them” are found in the two creeds used by the church in its worship and promulgated in the fourth century. But these were works of ecumenical councils, councils of the undivided church. Since 1054 and the division between East and West, no such council has been possible.
Therefore, while it is perfectly possible to hold such beliefs as the Immaculate Conception and the Assumption as Anglican Christians, I would suggest that they are best understood as “doxological,” not “theological.” In other words, they are best understood as remaining in the realm of prayer and praise rather than promulgated as dogma that is an authoritative principle considered as true and binding upon believers.
I would go so far as to suggest that, in any eventual reunion of Christians, nothing should be required of believers beyond that which was embraced by all prior to the tragic separation known as the Great Schism in 1054. In other words, unity in essentials … liberty in doubtful matters … but in all things, charity.