We use special pricing (and adding dates) a lot more than using a rule. So if I made a coupon code, with "stop further rules from processing" will it just make special priced products even lower basically ignoring the option?
Stop further rules from processing has no effect on the special price set at the product level. It only stops other rules of lower priority (ie higher number) from running. And it only works on same type of rule. Catalog rules can stop other catalog rules, and shopping cart rules can stop other shopping cart rules.
However, In the situation you've described, if the discount in your rule exceeds that set inside the product configuration special price, it will use your higher discount for special price instead.
So for example, if your product price is $10 and you make special price $9 at the product level, and then make a rule for 15% of same product it will show as $8.50 on frontend. If you make a rule for 5% nothing will happen, since the 10% discount at the product level is greater.
I've just tested this and my example is correct.