I have been building stuff with pallet wood for about 3 years now. I have yet to see a pallet that has been chemically treated. If you are concerned about chemically treated pallets, they will be marked with "MB" and those are not safe for home use. I personally have never come across one of those chemically treated pallets. All my pallets are marked "HT" for heat treated and are perfectly safe for home use.Pallet wood is chemically treated and not really considered safe. Yikes!
Of course, I also use common sense and if I find a pallet that has some oil or other chemicals spilled all over the wood, I pass on that pallet even if marked as HT.
If you know how to read the codes on the pallet wood, you should not have to worry about the safety of the unit. Sometimes you can save a lot of money by reusing that pallet wood and saving it from being dumped into a landfill as waste.