It depends on who you are asking. A debt collector will, of course, tell you that paying off your collection in full will immediately improve your FICO score. The truth, however, is a little different. In the long term, paid collections will reflect less negatively than open collections, but by paying a collection, you are essentially admitting that you owe and it wasn't mistakenly put on your credit.

Beyond the admittance of actually owing the debt, paying a collection will typically result in your score dropping.  Why?  Paying on the collection updates the status of that tradeline on your credit report. Recent activity is always weighed the most when determining credit score, while late-paying the collection will actually negatively impact your score temporarily. 

This is not always 100% accurate, as the algorithms that produce your credit score are closely guarded by the bureaus. In my experience, however, paying off collections typically takes 3 to 4 months before it reflects positively on your score.

The best way to get your FICO score higher if you have unpaid collections, is to request a letter of deletion in exchange for payment. Getting the collection removed from your credit will have an immediate positive impact.