Hi!

It should work.
How ever the log database should be shared.

There are two ways.
1)
Select one computer as database server where the logs are saved. You have SQL database server there ready if Cqrlog is installed (it comes from dependencies install).
You should generate a SQL user who has privileges to use SQL server. To do that open command console and type:

sudo mysql

When you get mysql prompt type following lines (copy /paste):

CREATE USER IF NOT EXISTS 'cqrlog'@'localhost' IDENTIFIED BY 'cqrlog';
GRANT ALL PRIVILEGES ON *.* TO 'cqrlog'@'localhost';
FLUSH PRIVILEGES;
QUIT;

You have to change localhost to IP address of your SQL server network card's address.
You may change username cqrlog and password cqrlog if you like.

Then you have to set the SQL server's firewall to access connections to port 3306. Maybe just from your local home network.
Allowing internet access is not safe, instead in that case internet access is needed you should create a VPN tunnel or a SSH tunnel to use.

When opening Cqrlog(s) in Database connection window do not check "save data to local machine" Instead fill your SQL server IP address, port 3306, username and password and press connect-button. You can also check remember me and auto connect
You should get connected from all PCs, including the SQL server PC itself.
Then all machines can use same log.

BUT !
Press Preferences/Program/Configuration storage settings - button with each PC where Cqrlog is running and select what settings are saved locally to each PC and what are common with all computers using SQL server.

2)
The other way, not so recommended, is to start Cqrlog in one computer using "save log data to local machine". When this PC is running you should not check that on other PC's. Instead write this "master" PCs ip address to Database connection window's server address and use port 64000 instead of 3306. User and password are 'cqrlog'.
Again you should release port 64000 of the "master" PCs firewall, and decide what settings are saved locally in every PC and what are common.

Bad side of this is that if the "master" Cqrlog dies all PCs lost connections to log database.
In case 1) it is enough that SQL server PC runs, even without having own Cqrlog at all.