Is something like this possible?

Centmin Mod is provided as is so such configuration is left to end users to figure out.

You can possibly filter out by url using an nginx map to a variable and edit access_log to exclude that nginx map variable for logging. Similar to how i excluded certain user agent/bots from logging in custom SSL log outlined at SSL - HTTP/TLS Protocol and SSL Cipher Usage Statistics Logging

So for your instance, as per Module ngx_http_log_module

so something like if request matches https://yourdomain.com/forum/index.php?liveupdate assign $nolog_liveupdate variable a value of 0 otherwise all other requests assign value of 1 (default)

The nginx map

Code (Text):

map $http_host$request_uri $nolog_liveupdate {
     default                                                1;
     "~https://yourdomain.com/forum/index.php?liveupdate"  0;
}

maps go in /usr/local/nginx/conf/nginx.conf within http{} context usually after hash bucket lines i.e.

Code (Text):

http {
 map_hash_bucket_size 128;
 map_hash_max_size 4096;
 server_names_hash_bucket_size 128;
 server_names_hash_max_size 2048;
 variables_hash_max_size 2048;

map $http_host$request_uri $nolog_liveupdate {
     default                                                1;
     "~https://yourdomain.com/forum/index.php?liveupdate"  0;
}

then use if conditional logging in access_log directive for your nginx site vhost config file which says log only requests that have $nolog_liveupdate value of 1 (which is all other requests exclude the liveupdate one which has value of 0)

so you change your nginx site vhost's access_log line from

Code (Text):

access_log /home/nginx/domains/yourdomain.com/log/access.log combined buffer=256k flush=5m;

to

Code (Text):

access_log /home/nginx/domains/yourdomain.com/log/access.log combined buffer=256k flush=5m if=$nolog_liveupdate;

Haven't tested it so you will have to test and re-config the mapping if not correct