How does that easement work for a ticket from Worcester?
You wouldn't be travelling to Alvechurch or Redditch,
via Ashchurch, would you?
Sorry I didn't read the easement properly and missed out the "via Ashchurch" part of it.
If the OP for example wishes to make their journey from a member of the Barnt Green group (which includes all stations on the southern section of the cross-city line but from Kings Norton northwards those stations are also members of the Birmingham group as well which may reveal more valid routes) then you can make your journey using only map CE, which allows you only one valid route- that being Barnt Green to Birmingham to Smethwick to Worcester.
This is probably because there are very few direct services from Barnt Green to Bromsgrove anymore- there only seems to be one in the southbound direction at 0743 arriving at 0805 into Shrub Hill. This service would be valid on a Barnt Green to Worcester ticket due to the fact you can travel on any direct services between the station on your ticket. The shortest route rule would also allow any stations on the Cross-City route connecting into that train travelling validly as well.
But to answer the OPs original question you cannot double back legally to Birmingham if you are travelling to Worcester.
EDIT-
If the OP however wished to make their journey via Ashchurch they would be able to use my original easement.
I.e. If they were travelling from Redditch to Worcester Shrub Hill, they could legally go Redditch to New Street to Ashchurch to Worcester, they would only be doubling back on the Redditch to Birmingham leg of the journey as going down to Ashchurch does not constitute doubling back as you don't pass through any other station again by doing so. I have no idea whether this is any quicker for the OP but opens up more options for them.