Perhaps
There is little evidence in Tolkien's writing, but I'm going to take a slightly different tack than Jason does in his excellent answer. I suggest that the minds (not just the bodies) of the Istari were affected by their incarnation.
The longest writing on the Istari is the essay in Unfinished Tales. The origin of the Istari is described like this:
For with the consent of Eru they sent members of their own high order, but clad in bodies of as of Men, real and not feigned, but subject to the fears and pains and weariness of earth, able to hunger and thirst and be slain; though because of their noble spirits they did not die, and aged only by the cares and labours of many long years.
Unfinished Tales Part 4, II: The Istari
I think that the fact that they were subject to the "fears" as well as the "pains and weariness of earth" suggests that their minds were not untouched.
A note attached to the essay tells us
For it is said indeed that being embodied the Istari had needs to learn much anew by slow experience, and though they knew whence they came the memory of the Blessed Realm was to them a vision from afar off, for which (so long as they remained true to their mission) they yearned exceedingly.
Unfinished Tales Part 4, II: The Istari
Another note describes a council of the Valar where it is decided to send the Istari to Middle Earth.
"Who would go? For they must be mighty, peers of Sauron, but must forgo might, and clothe themselves in flesh so as to treat on equality and win the trust of Elves and Men. But this would imperil them, dimming their wisdom and knowledge, and confusing them with fears, cares, and weariness coming from the flesh."
Unfinished Tales Part 4, II: The Istari
This passage not only mentions that the Istari are subject to the fears coming from the flesh, it states that their wisdom and knowledge are dimmed.
Conclusion
I think these passages suggest (but don't prove) that the minds, as well as the bodies, of Istari became "of the earth" (better not say human). Their memories are no doubt impressive, but may not be infallible.