The Hubble is in a 28 degree inclination orbit. The minimum inclination you can launch directly into from Balkinour (Tyuratam) is about 51 degrees. There can be some tricks such as the one gbaikie describes below that might allow you to achieve a lower inclination, but I doubt the Soyuz booster has sufficient excess delta-v to pull it off. Launching into an inclination lower than the launch site's latitude is a lot harder than flying to the equator and hanging a hard left turn. Given Balkinour's high latitude, I doubt you could reach the equator without achieving orbit. Getting into the correct orbital plane would be very tricky, too. Simply achieving the same inclination isn't enough.

If they could launch from the ESA site, it'd be a different story. However, that facility probably won't be ready for quite some time. Not only would they need to build the launch facilities (no small task), they'd need to have the capability to prep a Soyuz capsule for orbit. That'll take a while.