I can offer some very personal experience for you to semi-answer your question. If the negative information is DELETED, then yes you will see an increase in your score. Unfortunately, that is not always the case.
I had a collection agency hounding me for months to pay a collection (which was BS in the first place, but that's a completely different story!) I put them off, avoided their calls, but eventually caved and came to a settlement agreement. I asked them to assure me that once I paid the amount they requested, they would delete the item from my 3 bureaus. They said they would report "accordingly." That's corporate speak for we'll stick it to you every way we can!
I settled on an amount to the tune of several thousand dollars, but when it came time to delete the item, they became the ones who avoided my calls and didn't return my messages. They reported to the credit bureaus that the collection was "Paid in Full" but was "Settled for less than the original amount." This has almost the same (if not worse) devastating effect on your credit as the original mark because it shows future lenders that not only did you have a collection, but you only paid a fraction of the debt. The bottom line is that the item wasn't deleted and was still affecting my score!
So my credit score didn't improve AND I was out a couple G's. I'm a huge advocate of keeping my payments current and not getting into that situation again, but I think you'll find that unless you get it IN WRITING that the item will be DELETED, you're better off riding it out and keeping the money in your checking account rather then paying the collectors. They are under no obligation to delete an item even after it is paid and can leave it on your report for up to 7 (and sometimes 10) years. If it's going to be on there anyway, wouldn't you rather be the one holding the money!?!
If I had to do it again, I'd wait it out or get a definitive answer (again, in writing) from the collectors that the item will TRULY disappear.