In a word, no.
But remember that they do not have everything.
For many Illinois counties, the Family History Library does not have personal property tax records from the mid-nineteenth century and later. While most genealogical problems do not require the use of these records, there are times when these records are helpful in placing a specific person in a specific location at a specific point in time. There are other counties where court case packets have not been filmed and where tract indexes to land records are still accessible only at the courthouse.
The Family History Library is an excellent place to work on your research. But do not assume that because you have searched there that you have accessed everything.