The short answer is “not really,” or at least, it wouldn’t apply only to the Pope.
The passage clearly refers directly to the Old Testament priesthood (see, e.g., Leviticus 16) and indirectly to Christ, who is the fulfillment of Old-Testament High Priest (Hebrews 4:14).
Today’s priests and bishops do participate in the priesthood of Christ, and the Old-Testament priesthood was a prefiguring of the New-Testament priesthood. As the Catechism of the Catholic Church (CCC) puts it,
The liturgy of the Church, however, sees in the priesthood of Aaron and the service of the Levites, as in the institution of the seventy elders, a prefiguring of the ordained ministry of the New Covenant (No. 1541).
The ministerial or hierarchical priesthood of bishops and priests, and the common priesthood of all the faithful participate, “each in its own proper way, in the one priesthood of Christ” (CCC 1547, quoting Lumen gentium 10 § 2; the common priesthood applies to all Christians by virtue of their baptism, and the ministerial priesthood pertains to those who have received the Sacrament of Holy Orders).
Hence, all priests and bishops participate in a special way in the priesthood of Christ, a participation that is essentially different from that of the common priesthood. (See the remainder of CCC 1547.)
This participation applies to all priests and bishops, and bishops to the greatest extent possible, since they possess the fullness of the Sacrament of Holy Orders. (See CCC 1557.) It would be a mistake, however, to think of the Pope as a “super-bishop.” He is not: he is just the bishop of Rome, and by virtue of being bishop of Rome, he is the head of all his other brother bishops, and as such has authority over the whole Church. (See CCC 882.) But his participation in Christ’s priesthood derives from his Holy Orders, just as with all the other bishops in the world.
Hence, it would rather uncommon for Catholics to interpret Hebrews 5:1 as applying to the Pope.