How long an appeal takes, and when you actually see the money
Board decisions in weeks to months. The saving shows up on a bill a year later.
Two different clocks: the decision, and the money.
The decision
Board of Review decisions typically arrive weeks to a few months after filing, depending on county volume. PTAB takes a year or more.
The money
Illinois taxes are paid in arrears. An assessment appealed this year affects the bill you receive next year. So a successful appeal filed in the summer usually shows up as a lower bill the following summer, not as a refund now.
If you win at PTAB after paying
You get a refund of the overpayment, and it can take months after the decision to be processed.
Why the delay is not a reason to skip it
An assessment reduction generally persists into following years — it is not a one-year rebate. That is the fact that makes a modest saving worth the effort: it is the annual saving multiplied by however many years before your township next rebuilds the value.