The question of whether Boethius wrote his Consolation as a Christian should be resolved, it seems to me, not in a general fashion, but rather through a detailed study of how Boethius adapts, for his purposes, references and allusions to classical authors.
The specific question we need to ask is:
In these references and allusions, does Boethius use a manner of statement, or form of speech, that is best explained on the hypothesis that he is deliberately altering classical sources with a view to integrating them with Biblical ideas or themes?I see something of what I have in mind in an article by John Magee, "Note on Boethius, Consolation I.1,5; 3,7: A New Biblical Parallel" (Vigiliae Christianae, Vol. 42, No. 1. (Mar., 1988, pp. 79-82), which argues that Boethius' image of Philosophy in torn robes is meant to allude, in part, to the image of the tearing of the garment of Christ-- since that image was used by Augustine and other Fathers to represent the division of the true faith by heretics, yet Boethius likely viewed his own imprisonment as a result of the plots of heretics.
Gruber points out that the image has possible antecedents in Homer and Proclus. But, again, the key question is (the Baysian one of) whether Boethius uses this perhaps not uncommon image in a form that would be unexpected if he were drawing solely from these sources, but that would be natural if, on the other hand, he intended at the same time to suggest an allusion to a Christian image.
That is, we need to consider whether there are expressions in the text of the Consolation, which fall short of the rather explicit allusion to Wisdom 8:1 in III.12P, but yet which, through how they have been changed, indicate a subtle and pervasive adherence to a Christian viewpoint.
I have carried out no systematic study along these lines (yet does any such exist?). But here are three examples from my rather quick inspection, in this spirit, of simply Book I.
(1) (Boethius to Philosophy, I P4, 38)
instillabas enim auribus cogitationibusque cotidie meis pythagoricum illud e(/pou qew=| .Kirk and Raven give qeoi=j e(po/menoj as the original. A deliberate change to the singular may be explained, of course, by Boethius' wanting to make the maxim broadly consistent with monotheism. Yet note that the altered maxim at the same time reverberates with perhaps the most common exhortation to Christian discipleship, "follow Christ daily" (e.g. a)ra/tw to\n stauro\n au)tou= kaq' h(me/ran kai\ a)kolouqei/tw moi, Lk. 9:24).
(2) (Philosophy to Boethius, I P5 4)
si enim cuius oriundo sis patriae reminiscare, non uti atheniensium quondam multitudinis imperio regitur, sed ei(=j koi/ranoj e)stin, ei(=j basileu/j, qui frequentia ciuium non depulsione laetetur, cuius agi frenis atque obtemperare iustitiae libertas est.The Greek is a quotation from Iliad II, where Agamemnon urges the Achaeans not to compete for supremacy, as if they were all kings. Yet in its new context, where the quotation serves as a profession of monotheism, for which Boethius has changed the verb to the indicative (Homer has e)/stw), it now becomes similar to the Septuagint, Deut. 6:4: ku/rioj o( qeo\j h(mw=n ku/rioj ei(=j e)stin.
(3) (Philosophy to Boethius, I P5):
postremus aduersum fortunam dolor incanduit conquestusque non aequa meritis praemia pensari in extremo Musae saeuientis, uti quae caelum terras quoque pax regeret, uota posuisti.A strange prayer, on Boethius' part, quae caelum terras quoque pax regeret! Whatever its antecedents, did Boethius intend also that it resonate with: sicut in caelo, et in terra?
The question, I say, cannot be decided in any way but this. And one suspects that, when it is looked at in this way, we will find, not an absence of evidence of the author's Christian (or, rather, Biblical) viewpoint, but rather hardly anything except this.