Yes, but trews/triubhas does not mean trousers, as I discuss here. They appear to be a particular type of trousers, as described by Dwelly and typically worn by Gaels, usually tartan, and also used specifically for the tartan trousers used as uniform by certain former Scottish regiments.
I would not be so affirmative about the Germanic origin. Both Celtic and Germanic languages are of the Indo-European family. Latin "bracca" came from Gaulish "*bhrāg-ikā", also cognate with modern Breton "bragoù". It is rather doubtful whether these languages were influenced by Germanic.
I agree with you about not being so affirmative. I would not be so affirmative about where bracca comes from. If a word is only found in Western Europe then it probably isn't Proto-Indo-European, so most likely originates in some unknown language. But who can say if it went via Celtic into Germanic, or vice versa, or simply went straight from the unknown language into all the languages whose descendants are spoken in this part of the world?