Yes, this is one of many allegorical meanings attributed to the unicorn. Sometimes it seems that just about every possible meaning is attached to every possible creature, in the medieval mind. The unicorn's main associations are:
- power, as with any horned creature.
- purity: the horn was believed to have the power to magically purify water, counteract poison, and cure diseases.
- divine intervention, as the horn suggests divine power reaching, penetrating or transforming the mundane horse - resembling a ray of light striking the horse's forehead.
Much of this comes from classical sources, such as the Natural History of Pliny, which were familiar to Christians. Additionally, there are possible unicorn-references in the Bible which can be made to fit with these classical ideas. Saint Basil the Great makes this connection, for example in Homilies on the Psalms 13.5 (commenting on Psalm 92:10):
On the whole, since it is possible to find the word 'horn' used by Scripture in many places instead of 'glory', as the saying 'He will exalt the horn of his people' (Ps 148:14) and 'His horn shall be exalted in glory' (Ps 112:9), or also, since the 'horn' is frequently used instead of 'power', as the saying 'My protector and the horn of my salvation', Christ is the power of God; therefore, he is called the Unicorn on the ground that he has one horn, that is, one common power with the Father.
Other writers to link Christ to the unicorn include Tertullian (Adversus Marcionem 3.18, Adversus Judaeos) and Ambrose. The specific interpretation involving Mary's virginity and the conception of Jesus comes about a bit later, influenced by the Physiologus that you mention, an allegorical bestiary written at some point between the second and fourth centuries, and containing the legend of how the fierce and wild unicorn can be tamed only by a virgin (chapter 36). This, and subsequent bestiaries, developed a more elaborate version of the imagery. By the fifteenth century it could include Gabriel as a hunter who blows his horn to drive the unicorn into an enclosed garden (hortus conclusus) representing Mary's virgin womb. This is a merging of two separate artistic traditions - the unicorn hunt and the secret garden.
The dense web of symbolism is rather difficult to unpick. Because these traditions are essentially mystical, there are many things simultaneously represented or suggested. And so the purifying nature of the unicorn horn may be connected to Mary's virginity, Christ's purity, his purifying of the world, and even the transformative consecration of the Eucharist. The hunted unicorn may sometimes stand for Christ's death at the hands of his persecutors (Das Buch der Natur, Konrad von Megenberg, 14th century; Bestiaire Divine, Guillaume le Clerc, c.1210-1211). Or it may refer to (secular) courtly love as the powerful knight-unicorn chooses to submit to a virtuous and virginal lady.
This extravagance did not last, however. It was a source of mounting embarrassment that Christ was being represented by a creature whose existence was doubtful, and of course all this sort of imagery was unacceptable to the Reformation leaders. Within Catholicism, the last session of the Council of Trent (1563) passed a decree against superstitious or unseemly images, also ensuring that bishops would have the authority to suppress anything that was confusing, unusual, or tending to excite lascivious thoughts. This was backed up by detailed expert guidance in the following years, such as the De picturis et imaginibus sacris of Molanus (1570). He allows the hortus conclusus (but without a unicorn) for Mary, as well as other scripturally-supported imagery, such as the lily among the thistles or the city of God, but generally rejects more fanciful allegories and non-Biblical legends. And so unicorn-imagery gradually died out.
- The Unicorn Tapestries, Adolph S. Cavallo. Metropolitan Museum of Art, 1998.
- The Unicorn, Lise Gotfredsen. Abbeville Press, 1999.