I just learned I have an outstanding bench warrant in Michigan for child support arrears. I will send in a payment this week to begin processing a payment schedule. I've been out of work, couldn't afford payments and now I need to fly to Alaska to take a job offer. Can I still fly if the warrant is not yet removed even if I begin paying on it? Please help! This job will save my life!

Yes, unless you have hired an attorney or appeared before the judge the warrant is not going to just go away because you start to pay.
So you are going to have to appear in court and have the court approve and order a repayment But they will also have to agree to drop the warrant and any other punishment for the late paymets.

Where are you flying from, if you live in Oregon and are flying to Alaska, you should be OK, you may be detained ( miss a flight) but I doubt if Michigan will pay to have you bought back, but they are allowed to detain you from 30 mn to a hour while the state of Mich decides if they are going to come and get you.

Did you miss a court date? If its simply for back child support then you may be able to appeal it once you start paying it and have it dismissed depending on what grounds the warrant was issued and the circumstance that created it.