Does an unbaptized priest need to be reordained?

Canon Law seems to suggest so:

Present 1983 Code of Canon Law states:

THOSE TO BE ORDAINED 

Can.  1024 A baptized male alone receives sacred ordination validly.

The old CIC 1917 stating the same:-

De subiecto sacrae ordinationis.      

Can. 968. § 1. Sacram ordinationem valide recipit solus vir baptizatus...

 However, noted in Denzinger Pope Innocent II wrote:

741 Dz 388 [From the letter "Apostolicam Sedem" to the Bishop of Cremona, of uncertain time]

To your inquiry we respond thus: We assert without hesitation (on the authority of the holy Fathers Augustine and Ambrose) that the priest whom you indicated (in your letter) had died without the water of baptism, because he persevered in the faith of holy mother the Church and in the confession of the name of Christ, was freed from original sin and attained the joy of the heavenly fatherland. Read (brother) in the eighth book of Augustine's "City of God" * where among other things it is written, "Baptism is ministered invisibly to one whom not contempt of religion but death excludes." Read again the book also of the blessed Ambrose concerning the death of Valentinian * where he says the same thing. Therefore, to questions concerning the dead, you should hold the opinions of the learned Fathers' and in your church you should join in prayers and you should have sacrifices offered to God for the priest mentioned.--Denzinger 741

Taken from Patrologia Latina: 

Apostolicam sedem, venerabilis frater noster, ut debuisti, consulere decrevisti. (Et infra:) Unde inquisitioni tuae taliter respondemus, presbyterum, quem sine unda baptismatis extremum diem clausisse literis tuis significasti, quia in sanctae matris ecclesiae fide et Christi nominis confessione perseveravit, ab originali peccato solutum, et coelestis patriae gaudium esse adeptum, ex auctoritate sanctorum Patrum Augustini atique Ambrosii asserimus incunctanter. Lege, frater, super octavo libro Augustini de civitate Dei, ubi inter cetera legitur: “Baptismus invisibiliter ministratur, quem non contemptus religionis, sed terminus necessitatis excludit.” Librum etiam B. Ambrosii de obitu Valentiniani idem asserentis revolve. Sopitis igitur quaestionibus doctorum Patrum sententias teneas, et in ecclesia tua iuges preces hostiasque Deo offerri iubeas pro presbytero memorato.--PL 624

Granted, this is an argument from silence. It can be noted that Pope Innocent does not call into question the priest's ordination, although this was not the main subject. The Pope however does continue to call the unbaptized man a priest.

More investigation will be needed for the origins and interpretation of the Canons on a baptized male being needed for a valid ordination. Certainly for a sacramental marriage both parties need to be baptized, however does it follow for the priesthood which requires the physical contact of a bishop and words, analogous to baptism. In Acts 10 we see the people received the equivalent of Confirmation before water baptism.