Like I'm sure if a historian is speaking in Latin they'd pronounce Julius Caesar as Yulius Kaezar but would they do that in English classes/lectures, or use the commonly accepted pronunciation in English? How about more modern people like Charles De Gaulle, would he be pronounced Sharu Degah?
Speaking on behalf of the Latinists, if I may: No. My students would not know who the blazes I was going on about, and it would stall their learning.
Cf. Chichairo.
One of my old Latin teachers did, at one point, tell me that he opposed the idea that v=w for the sole reason that velle (to want) would be pronounced welly, and he wouldn't stand for that.
This is a problem that applies to names themselves, not just pronunciations! "Catherine" of Siena is Caterina; "Germany" is Deutschland. In general, the same principle for pronunciation is used that is standard for translating names. If there's a commonly-accepted English version--Catherine, Germany--use that. If there isn't, use the original--so, Katharina Tucher still.
It's the same for pronunciation. German doesn't have a "th" sound, for example. (Have you ever heard an English-speaker mention Martin Lutter?) Well, Elisabeth of Schönau and Elisabeth Achler are two medieval German holy women. The first has a fairly significant presence in medieval religious history and scholarship; the second REALLY does not. So I would say "Elisabeth" of Schönau with the th, but "Elisabet" Achler with a hard t.
I hope that helps!