No, Rome says it’s an unbloody sacrifice......you can’t have it both ways.
The full teaching:
The sacrifice of Christ and the sacrifice of the Eucharist are one single sacrifice: "The victim is one and the same: the same now offers through the ministry of priests, who then offered himself on the cross; only the manner of offering is different." "In this divine sacrifice which is celebrated in the Mass, the same Christ who offered himself once in a bloody manner on the altar of the cross is contained and is offered in an unbloody manner." (CCC, n. 1367)The same sacrifice. It is only made present in an unbloody manner. The Mass is a sacrament, i.e. an outward sign of an inward and invisible grace (St. Augustine). Thus in the Mass there is the unbloody outward sign which makes present the inward grace of the bloody sacrifice of Jesus on the Cross. Without this fundamental understanding of the sacraments you cannot understand Catholic teaching.