Short answer: Yes. I'm unfortunately not a professional historian but I've been watching this question and no one else has answered, and I think I can at least shed some light on this.

First, I can’t recommend Ian Kershaw’s book The End enough for a question like this. The entire point of the book is to explain why Nazi Germany fought on, far past the usual point of capitulation, until Hitler’s suicide, and it covers this kind of question beautifully.

Keep in mind that in 1944 there were no Allied troops on German soil. The Western Allies were occupied with pushing north through Italy and sweeping through France; the USSR was quickly reconquering Eastern Europe. Germany itself was not yet occupied. Meanwhile, Allied strategic bombing of German cities was accelerating, but the countryside was not intentionally targeted for bombing raids because it didn’t offer the necessary targets. Allied bombers were seeking to disrupt the German war effort by (1) destroying infrastructure that supported the military, e.g. factories and transportation, and (2) destroying civilian housing and facilities, which not only satisfied political demand for revenge against Germany and decreased general morale but also increased the strain on the German government. Bombing the German countryside didn’t do much to accomplish either of these goals. It’s also worth remembering just how inaccurate bombing was at the time: you needed a target roughly the size of a city, and if possible hundreds of bombers, in order to be reasonably sure you were going to hit what you wanted to. As a result, rural areas were noticeably better off than the urban locations that were liable to be flattened.

During all this, the German state and an admittedly-militarized society continued to function, to the point that it is outright weird, which is what Kershaw seeks to explain in his book. The Nazi German military fighting to the end is one thing, but (to your question) all through 1944 and literally up until complete disintegration of the Nazi state, the little things continued to work. Mail was delivered. Phones and telegraphs worked, to the extent telephone infrastructure hadn’t been bombed or could be repaired. Newspapers were published and distributed: the last edition of the Nazi newspaper, the Volkischer Beobachter, was dated April 28, 1945, only two days before Hitler killed himself. Radio worked all throughout, incidentally, hence Berlin’s ability to at least sporadically communicate with the rest of the country in May 1945. The Berlin Philharmonic provided its last performance of this era on April 12, 1945. Goebbels kept movie theaters open, to the extent that he could. Bayern Munich played local rival TSV 1860 Munich on April 23, 1945. So an outright Party organ like the Hitler Youth continuing to work somewhat normally is not that surprising. In fact, in the wake of the pivotal June 1944 assassination attempt against Hitler and as Allied forces closed in on German soil, the Party reasserted itself as a faction in German power politics. Martin Bormann became one of the most powerful figures in the state, and Nazi governors (Gauleiter) gained sweeping powers to organize civil defense efforts.

As an explanation for this, it is crucial to keep in mind that the Nazi political leadership was massively influenced by the experience of collapse and capitulation in 1918, and was commensurately motivated by the desire to make sure that didn’t happen again. There are a multitude of examples – the SS’s original purpose, overlapping with its mission as a Party bodyguard, was to serve as a body capable of quickly crushing a 1918-esque revolution, to note just one – but the overall point most relevant to your question is that, at the highest level, the Nazi leadership was keen to ensure that civilian life was cared for to the fullest extent permissible by the war effort, so as to help prevent an uprising like the one that ended the German war effort in 1918. The “stab in the back myth” is fairly familiar, but in the context of your question, the antisemitic and anti-liberal elements are secondary to the point that the home front did in fact rise up and made it impossible for Germany to continue that war. Hitler in particular, and to a lesser degree his various subordinates, were haunted by that and went to extreme lengths to ensure it could not happen again. (They succeeded.) This was why the leadership insisted on keeping civilian comforts and, where possible, the ordinary functions and ceremonies and window dressing of the state functional until it was no longer physically possible.

To summarize, in 1944 the German state and German society was highly militarized to support the war, but life went on, in large part because the people controlling Germany were working very hard to ensure that it did. Making things look as normal as possible on the home front was a pretty massive priority for the government, which continued well into 1945. Party organizations, in particular, were reasserting themselves at the time, at the expense of competing institutional pillars like the military, SS, and non-Party civil leadership, due to changing priorities in the leadership. And not only were Allied soldiers not yet present on German soil, Allied bombing did not generally touch the countryside, for various strategic reasons. So the Hitler Youth still holding camp, or whatever it is they were doing, at that time and in that place is 100% realistic.