Yes. They can go to Court - the Court documents are sent to your last known address so you may not receive them. The ccj is none the less valid. If you find out about it after it has been made you can apply to have it set aside on the ground that you did not know about it. BUT the Court is only likely to grant such an application if they can be satisfied that the outcome - had you known about the case - would very likely have been different. In other words, that you had a reasonable defence to the claim. As you clearly acept you owe the money it is most unlikely the ccj would be set aside.
If the ccj is made without you submitting an income & expenditure form & a payment offer the judgement will be for the total amount to be paid forthwith. You will then be in default of the judgement from a few minutes after it is made & the creditor could take enforcement action (bailiffs, attachment of earnings, charging order etc.) if he knew where to contact you.