NO is the general case
Boiler engineers are highly qualified on matters of gas safety and in some cases mains electricity - it's a rare thing to find one who has more than a basic understanding of electronic circuits
A person very familiar with a particular circuit board may under some circumstances be able to recognise for instance, a scorched component showing signs of overheating or a bulging capacitor about to fail but to be able to do this the components must be inspected - most control boards have a plastic lid with a label warning Warranty Void if cover removed - so most of the pcb is invisible.
In some circumstances the electronic behaviour of a circuit board may show evidence of begining to fail - a timer circuit operating too soon or too late perhaps but if the system is working this is no guarantee that things will become worse.
I began my electronics career in 1962 and have never been able myself, nor have I ever met any other service engineer who had the ability, to predict faults. Any engineer who could do this would be worth millions.
There are some very sophisticated and complex automatic test stations that may come close to accurate prediction of failure but not a timescale prediction.
Faced with a known, defective PCB all you can tell is that it's broken - it's virtually impossible to backward predict the point in the past when the failure began to happen. Faced with a working PCB it's virtually impossible to predict the point in the future when it will fail.
A statistical Mean Time Before Failure (MTBF) analysis will give an average number of hours that a population of PCBs will last but I doubt that even the manufacturers bother with working it out.
Unless the engineer had some evidence of the erratic behaviour of your boiler over the past 2 months then he is not in a position to make such a statement. "It may have been behaving incorrectly for some time." is the best he could say.
Peccavi
January 2010