No, you cannot be forced to buy the car, you can walk away from the sale....if you've not already signed.
Hard to tell exactly your status because you suggested that you already signed. If its a done deal, and the contract contains a BA clause you just discovered, you're bound by the agreement full stop.
Your state MAY have a short period during which you may back out, check with an IL attorney ASAP.
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Your question is a little confusing. If you already signed a contract to purchase, then you are not in a position to refuse to execute a binding arbitration agreement if it is in fact part of your contract.Ask a similar question