Oh boy, I can finally put my graduate research to use so I'll just rant.
So over the past few years I've been through a lot of material on German Ostpolitik during WWI. Interestingly, I have yet to find a single scholarly work or primary soruce which mention the words "United Baltic Duchy" (Vereintiges Baltische Herzogtum) (or mention it with a primary source referenced to back it up). Fischer doesn't mention it, Baumgart doesn't mention it. I have no idea where the term originated. I question a lot of the things which the wikipedia article presents as fact. I could see a state like this emerging from a German victory, but as for the name itself, I'm not sure about it.
The duke-elect was duke (titular) Adolf Friedrich of Mecklenburg
As far as I know, Adolf Friedrich zu Mecklenburg was never elected as duke. That's not to say he wouldn't have been one of the main candidates for such a throne had it been made. He was president of the "German-Baltic Society" which was formed in mid 1917, and was in contact with notable Baltic Germans. So the House of Mecklenburg had an interest in the region, but so did Prussia.
The Baltic Germans might have wanted the UBD to become part of Germany. But that wasn't the plan in Berlin.
Except the whole idea of the Baltic Duchy project is that it joins as a constituent state of Germany, not as a colony. Or, originally, as a part of Prussia in personal union, but that still makes it a constituent state of Germany, not a colony.
There was no singular plan in Berlin, there were multiple competing views on the situation, the Prussian province/personal union idea was advocated for mainly by Ludendorff's circle. Kaiser Wilhelm did scribble this on a newspaper article , which I unfortunately cannot show my photo of.
"Nonsense! The Baltic is one, I will be its master and tolerate no opposition. I have conquered [his emphasis] it, and no lawyer can take it from me!
Balticum is one, under Prussia's king in personal union, who conquered it! As under Frid. Rex! [?]"
(It's important to note though that Wilhelm was very easily swayed by whoever was around him at the time and de facto did not have the final say on foreign policy matters. Here he is basically just parroting lines OHL had been whispering into his ear.)
There was also the idea of giving it to one of Willy's sons (throughout the war pretty much all of his sons were proposed to be made the monarch of some fief)
But the Foreign Office, members of the Reichstag (such as Ebert), all had differing views on the region. The Baltic Germans themselves have ideas, but there were differences in opinion amongst them too. Paul Schiemann, a major player in the Baltic German community, was expelled from Riga in 1917 for anti-knight views and advocating for independent Baltic states, and the Germans banned him from coming back until October 1918. There was very little support for something like the United Baltic Duchy among the Latvians and Estonians.
Finally someone recognises Latgale would have been part of this entity.
I doubt that the local people of Latgale will have any say in that at all. The borders will be set by the Germans and Russians at the negotiating table. However, the Brest-Litovsk treaty is not clear about it... According to the Wikipedia article in the OP, Latgale will be one of the seven cantons of the UBD.
In the original Treaty of Brest-Litovsk signed in March 1918, Russia ceded Courland (plus some bits of Livonia around Riga), but not the Livonia and Estonia governorates, which were to remain occupied by Germany "until order is restablished." This was basically a half-measure brought about by disagreements between German leadership. The military (OHL ie: Ludendorff, Hindenburg, etc.) pushed for Livonia and Estonia to be ceded like Courland, but the Foreign Office (AA) was opposed to this, thinking that it would cut Russia off from the Baltic Sea and create a permanent threat to St. Petersburg, ensuring that future relations between Russia and Germany would be strained.
Russia only renounced sovereignty over Livonia and Estonia in the German-Soviet Supplementary agreement signed in August 1918.
The OHL was apparently keen on shifting the border of Livonia eastward into Latgale for defensive reasons. This issue was apparently brought up at the only meeting of the German-Russian boundary commission established by the Brest-Litovsk Treaty in May 1918, and the Russians were very opposed to shifting the border eastward. Unfortunately I haven't had the chance to look at this document yet though, so I can't provide specifics.
On the other hand, there is a note exchanged between Joffe and von Hintze that was added as a secret protocol to the August supplementary treaty which alludes to the border to be determined by the commission. It seems to imply borders which match those of the Russian governorates (along the line Lake Pskov-Lake Luban-Liwenhof (Livani)) but at the same time taking the "defense of Livonia" into consideration in the area Southwest of Lake Pskov. I would say this represents the AA's view on the matter.
How viable would this United Baltic Duchy have been if Germany had won World War I
In short, I don't think the outlook would be good for it. It would be propped up by German bayonets, and if this is a 1918 victory (which I kind of assumed it was, so apologies if not) the guys carrying those bayonets want to go home, not stay in the Baltics. Without greater consideration to Latvians and Estonian national aspirations, it would probably fail.
Or are there other possibilities?
The state proves unfeasible due to Estonian and Latvian discontent. Germans fall back to just Courland and Riga (possibly stay in the Moonsund as well), and Livonia and Estonia are ceded back to Russia.