No, please don't send that letter. If there is an employee's handbook with a written policy on solicitations, by all means satisfy your curiosity. Other than that, just decline. Solicitations of a recurring nature (scouts, kids' fundraisers being conducted by parents), just decline with a "no thanks, I'm stocked up from my neighbors'/siblings' kids" or some such.
You can decline betting pools on principle and you can respond to requests for religious donations (frankly, I'm stunned) with "Sorry, but I'm already at my limit for church donations," even if your limit is zero. If there is an official "cup and flower" fund...the kind of thing that all contribute to so that flowers are sent on the appropriate life changing occasions (hospital stays, funerals, etc.), by all means, participate.
Please don't begrudge the potlucks! They are a whole lot cheaper than an obligatory trip out to lunch or dinner or kicking in for a catered meal. You don't have to go any more elaborate than a box of donuts or a bag of chips and let those who really enjoy that stuff get whipped into a frenzy out-competing each other with their recipes.
Every place I've ever worked had very strong written policies against solicitions and in particular those by supervisors made to subordinates at any level. Some places had the "cup and flower" type fund for flowers as I described above. It was even very rare for a well-known cosmetics company catalog to be left out on the break room table for people to place orders.
My betting pool story. DH and I simply.do.not.follow.sports. One year at my place of work, I was approached to put money into the pool for the Super Bowl. The guy collecting nearly passed out when I asked in all oblivious innocence, "Who's playing?" No, I did not participate in the pool and neither was I invited to again.