Unless you allow the possibility of launching from a launchpad that didn't exist at the time (and the Soyuz pad in South America never had the infrastructure for crew launches anyway) - placing your question into "completely hypothetical" mode - the answer is no, as stated in the CAIB report. They didn't even consider rescue by expendable vehicle anyway, just launch of supplies.
There has been some discussion regarding the possibility of sending supplies to Columbia using an expendable launch vehicle – to lengthen the amount of time available to execute a rescue mission. Because of Columbiaʼs 39-degree orbital inclination, an expendable launch from a launch site with a latitude greater than 39 degrees would not be able to reach Columbia. This rules out a Soyuz/Progress launch. There was an Ariane 4 in French Guiana that successfully launched an Intelsat satellite on February 15. The challenge with developing a supply kit, building an appropriate housing and separation system, and reprogramming the Ariane seems very difficult in three weeks, although this option is still in work.
CAIB report Volume 2 Appendix D.13
It would also have been impossible for Soyuzes from the ISS to reach Columbia. The inclination difference between the ISS and Columbia's orbits was about 12 degrees. At that altitude 1 degree of plane change takes about 120 m/s delta-v and a Soyuz-TMA is capable of a total of about 390 m/s delta-v.