That wouldn’t work; not even close. Particularly if you’re interested in picking up smallish effects (say, a 50% increase in deaths). It actually is quite complicated.
You need to know how many people were vaxxed at that time, preferably broken down by age, or at least by age group (say, 75-79, 80-84, etc). You need to know the exact followup interval - sounds like about one week - and how many people died. Then you need to know the all-cause mortality risk over the same week in previous years, again broken down by age.
Those numbers will allow you to calculate how likely it was that the post-vaccination outcome was due to chance.
The statement from the CECC is not false exactly, but it is, at best, meaningless. It is not possible to state categorically “these deaths were not associated with the vaccine”. That is essentially unknowable. All you can do is calculate the aforesaid probability.