It is always worth trying everything!
Experience shows you win some, you lose some. But if you dont try then you are guaranteed not to find anything!
Thats my policy.
Over the years whilst doing family history research my brother and I have written (yes, most of it done before email invented) to all sorts of places. Many we heard no more from, but just occasionally it paid off.
I remember finding on a gravestone that a distant rellie was "buried in Buenos Aires". This was news to us, a poor Ag Lab family where the sons worked the land and the girls went into service. One daughter had never married and it was her that seemed to have saved up and spent her savings on the headstone for her parents and some siblings grave, and she had mentioned this sister on it.
We wrote to "The British Consulate Buenos Aires", not even having a proper address, asking if they had any details of where she might be buried. They passed the letter to the person in charge of a British Cemetery in Buenos Aires. He sent us a lovely reply along with a photo of the gravestone - our ancestor was a servant to a well to do family that went to BA, and she was buried in their family plot with an inscription added to the gravestone "our faithful servant ...".
All a result of a 'shot in the dark' letter.