Yes.
I have a professional upholstery steamer that I also use for cleaning older soiled fabrics. Clean and vacuum the fabric first. Have clean cloth towels that are absorbent. Those big box store Terry towels don't work well IMO until they have been washed several times in fabric softener. Use Spray & Wash Pretreatment lightly and allow it to work on the embedded dirt. Next, steam a small area. Then use the towels to blot it dry. Reapply the steam, and/or the Spray & Wash and steam. If you have an extractor, that works well for quickly drying the fabric however you need to use the towels to transfer the dirt from the seat cover to the towel. Try not to rub the fabrics as it tends to grind the dirt into the fibers. Repeat as necessary until it all comes clean.