I was reading an old NYT Article, and it suggested that there is value in that police officers who are cross-trained as lawyers. Although rare, the article suggested that most who go through this route are retained as in-house counsel rather than practicing lawyers and judges. So I ask, can these police-lawyers ultimately practice law in the sense that they have the powers to investigate, arrest, try, and (if possible) judge?
Lawyers neither try nor judge cases; they advise and argue them. Criminal cases in jurisdictions based on British law (which seems to be what you are asking about) are tried by prosecution and defence both putting their best arguments to the court (either a judge or a jury) who then reaches a verdict. There is no reason why the prosecuting lawyer should not be a police officer (assuming he is properly qualified), though in reality 'prosecuting advocate' is a full-time job, so the officer would need to transfer to the District Attorney's office or something similar.
Actually, such an officer would be wasted by a transfer to advocacy. Somebody who knows not only what evidence is inadmissible and the leading cases on permitted searches but also where the local crime blackspots are and which officers, likely to fall apart on creoss-examination, should not be put up as the only witness is valuable enough that the authorities (whoever they may be) will make considerable efforts to use these talents to best effect.