Should I submit my book to free distribution sites for exposure?

As long as your book isn’t in KDP Select you can sell it anywhere you want. Be aware, though, that Amazon will price match so if you give it away in one spot and Amazon finds it, then they might reduce the price to giving it away on their platform as well. (Which can be useful if you want a permanently free lead generator…)

One option you could consider is to give away portions of your book at those free distribution sites and have links for where they can purchase the full book. If you are in KDP Select, then the book can not be substantially similar if distributed anywhere else; Amazon’s Terms of Service do not really go into more detail than that about what constitutes something that is substantially similar but I imagine that anything that contains more than 10% of the book (what is shown in the preview on Amazon’s site) probably would not work.

If you are not in KDP Select, then you just need to be careful to make sure that it is exceedingly obvious that it isn’t the full work; I remember a story about a mainstream author who had a sample that he was giving away get price-matched by Amazon despite it saying that it was a sample chapter, and he wound up having to give away somewhere in the high-5 figures or low/mid 6-figures of copies of his book (I forget which.)  I never did hear if his lawsuit went anywhere; it hadn’t the last I’d seen anything about it.