Yes I would think so, lots of courts and back to back houses. You can see half New St station top right, beyond which would have been the city centre.
Not sure if you can make out Hurst St - it crosses Bromsgrove St to the left of the pink dot - but if you follow it up, you come to Inge St (first road) and on the corner there are some surviving back to back houses...
Explore 200 years of working peoples' lives on a guided tour of the Birmingham Back to Backs, a carefully restored court of houses built literally back-to-back.
www.nationaltrust.org.uk
I don't imagine houses would have looked as clean and tidy in the late 18th century though.