No, Bazile, normal limitation periods apply.
The point of Trustee Act notices is to protect the executor personally. So if an exec advertises and no one comes forwards within the time limit, he or she is able to distribute to the beneficiaries. After the expiry of the time limit a creditor may still claim his money but the executor has no personal liability for the debts - it is a complete defence to any claim against the executor (assuming he had no knowledge of the debt). If the executor does not place the adverts, the creditor should go after the executor personally - generally, the exec will then claim the money back from the beneficiary.
The adverts are all about protection for the executor. They do not have the effect of extinguishing the debt. However, if the creditor fails to do anything he may find himself met with a limitation defence. (Different limitation periods apply depending on the nature of the debt and once the period has expired the debt is statute barred. There are also equitable defences but I suspect a legal essay on these is not going to help the OP).