Should physical training from an osteo help with chronic Achilles soreness? Mostly happens the day after running. I wear orthotics.

Not sure. Im not sure what type of training from an osteo you are doing. Usually the problem can be calmed with physical therapy modalities, ice and nsaids if it always happens after running you may need to change your shoes, run less or work more on calf/ achilles stretching.
Achilles. Eccentric calf muscle exercises are the best training for chronic achilles tendinosis.