Mary
Here is what I found in the transcripts mentioned above.
BaptismsThe bad news is that I could not find any reference to
Thomas c1808 who appears on the censuses with his parents but the good news is that I did find the following, which seem to bear out your suspicions :-
1806 January 5th
William s of William and Elizabeth Hodgets.
1814 June 19th
George s of William and Elizabeth Hodgetts Nailer
1815 November 12th
James s of William and Elizabeth Hodgetts of Silver Street Nailer
1820 May 23rd
Benjamin s of William and Elizabeth Hodgetts of Silver Street Nailer.
So, there are two more sons (George and James) and the fact that Thomas is missing may also mean that there could be others who are also missing from the transcripts but I have no way of checking that for you. You might have to try the links that I gave you above unless someone else who actually lives in the Kings Norton area could check for you.
I also checked the Burials from 1800 to 1844 but I did not find any relevant ones. I also looked to see if I could find the Marriage of William and Elizabeth between 1798 and 1806 but I could not see it. Sorry.

DS