Whilst you are allowed to sign players on on the day, it is not something that is either recommended or encouraged by the League as it does have its pitfalls.
As you will be aware, before you sign a player on on the day, it is suggested that you contact the League Registration Secretary to check that the player is not registered with another club.
If the Registration Secretary is unavailable, and you cannot contact another League Officer, then any player you sign on on the day, is signed on AT YOUR CLUBS RISK.
If it is subsequently found that the player is already registered with another club or is otherwise ineligible to play for you, then your club will be charged with playing an ineligible player. You cannot use the excuse that you could not contact a League Officer to check his eligibility as mitigation.
You have until 17:30 on the day before a match to seek to register a player via WGS, and when carrying out this process any problems should show up.
It is therefore strongly recommended that you do this to avoid any potential problems.