It looks like it does, which depending on your goal is either helpful or part of the problem. By default processes should inherit their parent's oom_score_adj. If I exit out of firefox completely, then start it up (with no saved tabs), this is the behavior I see:
$ firefox-esr& PID=$!; choom -p $PID -n 42
[1] 105360
pid 105360's OOM score adjust value changed from 0 to 42
$ for p in $(ps --ppid $PID -opid --no-headers $PID); do printf "%3d" $(</proc/$p/oom_score_adj); ps -opid,comm --no-headers $p; done
0 105360 firefox-esr
0 105425 Socket Process
167 105451 Privileged Cont
0 105456 RDD Process
100 105495 WebExtensions
0 105524 Utility Process
233 105534 Web Content
233 105542 Web Content
233 105549 Web Content
See how each firefox process has a different oom_score_adj with Web Content being more likely to be killed than other processes (233), and none of them have the value that the process was started with (42). This is Firefox 140.11 ESR running on Debian 13.
Yes this would be nice. Or maybe the OOM system would have two other files, /sys/oom/kill_first and /sys/oom/kill_never which would solve the problem more directly for the majority of cases.
I should really send a patch rather than complaining ...