You can always write a letter but your relative's failure to appear timely for his sentencing could lead the judge to believe that he is not a good risk for work release and / or that he is not taking his situation seriously. Why don't you talk with the relative's lawyer about the situation and see if there is anything the lawyer feels that you can do to help.
Yes, you should write a letter, but the defendant needs to write one too. Explain the missed court date and also explain in detail the need for work release, ie family, job, responsibilities, etc. A letter from the Defendant's employer would be very helpful too. These letters don't need to be fancy or include any special "legaleze" but should explain why work release is so important and why the Defendant would comply with such a sentence.