W.I. The "Deutsch Ordenstaat" is fully incorperated in HRE?

What if the lands conquered by the Teutonic Knights would become part of the HRE was there any chance that they still would be a part of it when the HRE ended?
Would there also be a much stronger germanification of the baltic?
 
I'm no expert on the Knights, but as far as I understand there is a very big problem. To be part of the HRE you have to be a vassal of the Emporer, while the Teutonic Order is under the authority of the Pope. Considering the conflict of interestes that define the relationship between Pope and Emporer during the Middle Ages that's a hard compromise to make.
 
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