Would calcification of the soft tissues show clearly on xray, or mri, for example stiffness in thoracic spine due to spondylitis?

Usually but always: Calcifications will show up on x-ray if there is enough of them. MRI doesn't show calcifications well. In the case of spondylitis, depending on the cause, there could bone erosions (loss of calcification), no calcifcation or abnormal calcificaion. A radiologist is trained to look for these things especially if spondylitis is listed in the diagnosis.