A quick overview of the process:
Once an executor is named, the will is given into the court. Usually preliminary letters are issued. What this means is that although the will has not yet been admitted to probate, the executor can start gathering the decedent's property to be distributed later. The executor uses the preliminary letters to close all accounts, and potentially sell property that is not specifically devised in the will. At this point a list of distributees is constructed, and each receives a waiver. They either waive their right to challenge the will, or they receive a citation, and are given the opportunity to challenge the will in court. Once all waivers are received, if applicable, the will is admitted to probate, and the executor can distribute the property.
From the time the estate is opened, all creditors have a certain amount of time to demand payment from the estate. Not sure about Connecticut, but in NY this period is seven months. That means that even if the will is entered to probate, the executor still usually waits this period of time before distributing the property because if it is not paid by the estate, the executor can be held personally responsible for the debt.
As far as "working on the estate," the executor must do the following with the money from the estate:
1. pay funeral costs
2. pay lawyer fees
3. pay creditors in the allotted period of time
4. calculate decedent's income tax for the year and put this aside
5. pay estate tax (though most estates are exempt)
6. calculate executor's commission
Aside from funeral costs, these things are typically done AFTER the will has been entered into probate, which results in a lag period between the time the will was probated and the distribution of property.
I hope that answers your question.