I read in an (unknown) aircraft accident investigation book that NASA engineers wanted to use DOD earth observation satellites to check for damage on the Columbia Orbiter during STS-107. This did not occur due to what seemed like pure bureaucratic ineptitude by upper management.
This question also asserts that such a satellite was used to photograph STS-1
A comment by @Organic Marble on an answer to the above question also asserts such a plan was concocted for STS-107:
there were several attempts including at least one by Wayne Hale to image [Columbia] using DOD assets. But Space Shuttle Program management stopped them -Organic Marble
Had an attempt been made, would it have been possible to photograph the underside of the orbiter with high enough resolution to conclude re-entry was not possible?
Given that the Shuttle orbiters had limited orbital maneuvering capabilities, and STS-107 had not had such an encounter planned (unlike STS-1), it seems like it could have easily taken too long for the "stars to align" and have a close enough encounter to effectively image Columbia.
EDIT: Additional detail on the proposed attempt from Wayne Hale's "How We Nearly Lost Discovery"
Engineers made three separate requests for Department of Defense (DOD) imaging of the shuttle in orbit to determine damage more precisely. While the images were not guaranteed to show the damage, the capability existed for imaging of sufficient resolution to provide meaningful examination. NASA management did not accede to the requests, and in some cases intervened to stop the DOD from assisting. The CAIB recommended subsequent shuttle flights be imaged while in orbit using ground-based or space-based DOD assets. Details of the DOD's unfulfilled participation with Columbia remain secret; retired NASA official Wayne Hale stated in 2012 that "activity regarding other national assets and agencies remains classified and I cannot comment on that aspect of the Columbia tragedy".