Would I be wasting my time?
Yes!
Graves in front of the church are few now. many headstones have been used for paths, or lining the sides of the pathway, often broken, some barely legible now.
The churchyard to rear was an overgrown brambley jungle the last few time I visited. The garden of remembrance is tidy'ish, but the rest needs a machete & weedkiller to access and as is usual with churches, graves are not in any sort of date order, being reused many times over the years.
However, a visit on a sunny day is pleasant, and if you happen to hack at some weds or brambles it wouldn't hurt!
There used to be a partial listing of recorded headstones in the churchyard in the Birmingham Library, but I think it was compiled in the 1930's or thereabouts?
Brian