Absolutely. In NJ there is case law on this. The debt will also survive foreclosure, so that no matter what happens, the dues will need to be paid for clear title. Keep in mind, that once the management company files foreclosure it also become public record.
Yes if they put a lien on the property and don't get payed, after a period of time they can foreclose , but if you have a mortgage on the property that company will step in and satisfy the lien because they don't want to loose the property and its position.