The Summa answers this nicely with a resounding, "Absolutely not." I'm lazy, so I'll just put Part III Question 46 Article 4 Objection 1 here:

As Chrysostom [Athanasius, Orat. De Incarn. Verb.] says: "Christ had come in order to destroy death, not His own, (for since He is life itself, death could not be His), but men's death. Hence it was not by reason of His being bound to die that He laid His body aside, but because the death He endured was inflicted on Him by men. But even if His body had sickened and dissolved in the sight of all men, it was not befitting Him who healed the infirmities of others to have his own body afflicted with the same. And even had He laid His body aside without any sickness, and had then appeared, men would not have believed Him when He spoke of His resurrection. For how could Christ's victory over death appear, unless He endured it in the sight of all men, and so proved that death was vanquished by the incorruption of His body?

The Summa answers this nicely with a resounding, "Absolutely not." I'm lazy, so I'll just put Part III Question 46 Article 4 Objection 1 here:

As Chrysostom [Athanasius, Orat. De Incarn. Verb.] says: "Christ had come in order to destroy death, not His own, (for since He is life itself, death could not be His), but men's death. Hence it was not by reason of His being bound to die that He laid His body aside, but because the death He endured was inflicted on Him by men. But even if His body had sickened and dissolved in the sight of all men, it was not befitting Him who healed the infirmities of others to have his own body afflicted with the same. And even had He laid His body aside without any sickness, and had then appeared, men would not have believed Him when He spoke of His resurrection. For how could Christ's victory over death appear, unless He endured it in the sight of all men, and so proved that death was vanquished by the incorruption of His body?

I think that pretty much sums up that Christ:

1. HAD to die
2. HAD to die violently
3. The violence MUST have come by man.

I suppose that strictly speaking it would be possible to have all of this happen with no blood being spilled, but that is not the theology of Aquinas. Article 1 makes it clear that his blood was shed and in Article 10 he cites the book of Hebrews and notes that Christ could not have fulfilled the law save by an immolation — something which requires a good deal more than one drop.