A rosary is mainly to assist in counting the prayers of the prayer that is « the rosary ».
You can pray the rosary counting on your toes and fingers if need be, as I’m sure many a martyr has done while awaiting the crown of martyrdom in some squalid prison. God understands.
And if you are eager to pray it before having the chance to have it blessed, then go ahead! God will appreciate your zeal in prayer!
Of course having one blessed can make it very special. Even though I rarely pray it (I’m more into the Liturgy of the Hours), I have a nice olive wood one blessed for me by an African monk at Subiaco that I treasure and is hanging in my oratory.