Should transition words (in addition, furthermore etc) be used to start paragraphs?
Does it show sophistication?
I'll address the second question first and say I think that nothing is inherently sophisticated. Like, using furthermore doesn't mean you're writing with sophistication... It just means that furthermore is in your vocabulary. I guess I see sophistication holistically (as the examiners should be looking at it)... A terrible essay that has 'juxtaposition' in it doesn't become a sophisticated essay because of the word. Sophistication shows sophistication. I'm talking about a variance in sentence length, great expression and articulation that leaves the reader with no questions, unhindered flow etc. Not a good word here or there.
Would I personally use those words at the beginning of a paragraph? No, I don't like it. I think Lollymatron would disagree - she said to me earlier she uses conjunctions at the start of paragraphs to improve the flow of her essay. I had a personalised way of writing topic sentences that I really liked, and they never included any conjunctions or transition words at the beginning. Reading an essay, I would also dislike seeing them used at the beginning of a paragraph - still a matter of preference! It wouldn't make a 10/10 less likely (if I were the one marking the paper), because as aforementioned, one thing doesn't automatically make the essay good or bad, they should be viewed holistically.
So,
Can they be used? If that's your inclination.
Should they as a strategy to demonstrate great English skills? Not as a matter of course.
Edit: I lied, I sometimes used 'however' as a starter for my third paragraph. Again, preference.