I cannot answer your question because it depends on whether or not the mobile phone company has reported the fact that you owe it money to the credit reporting agencies. If it has, it also depends on how that negative information has affected your credit score and on the potential landlord's standards for who it rents to. In other words, some landlords may only rent to individuals with good solid credit scores, while others may not have a problem renting to people with lower scores.
Bear in mind too that even if the mobile phone company has not reported your delinquency to the credit reporting agencies, if you have negative information related to other accounts in your credit history, like late payments, collection accounts, etc. that information could affect your ability to rent a place to live.
By the way, if you do end up being sued for your mobile phone debt and you lose the lawsuit, the fact that there is a judgment against you will be very damaging to your credit history. Also, the phone company will be entitled to collect on the judgment by garnishing your wages, taking money out of your bank account, putting a lien on an asset that you own, and so on.