Yes, but I think run_init is supposed to be run with init scripts, not the respective daemon:
run_init /etc/init.d/httpd
On the other hand, httpd's init script doesn't have initrc_exec_t, but its own "initrc_exec_t subtype":
# ls -Z /etc/init.d/httpd -rwxr-xr-x. root root system_u:object_r:httpd_initrc_exec_t:s0 /etc/init.d/httpd
So best would be to just do "service httpd start", which will call the corresponding init script, where the proper transitions will happen.
Best regards, Michael