If you have good enough performers, unfamiliarity with the language won't get in the way.
It might seem a bold assertion, but there's a reason that classically-trained Shakespearian actors are often cast in sci-fi shows (Patrick Stewart and Ian McKellen as perhaps the most famous examples). They're trained to convey more information through intonation and gesture so that you don't need to know the words they're saying, which translates well to performances in invented languages.
I tend to agree (Alec Guinness being another great example), though I think it is also about how big a deal live Shakespeare was in Britain in the eras those actors came up. A lot of good British actors were in Hamlet because they were talented and of age.
It'd be extra convincing if there were more non-Brits with Shakespeare backgrounds that became big Sci Fi actors to point to. There are American Shakespeare companies or performances, but it's a much smaller deal.
ETA: another source of great sci-fi actors was Hammer Films, which produced Christopher Lee and Peter Cushing. Great American sci-fi actors come from more backgrounds because there's more acting jobs in America.
David Tennant (THE Doctor) is performing Macbeth at Donmar Warehouse in London this winter. One show basically ticks three boxes (actor, play, and theatre) for my wife and her Shakespeare fandom. So it's a 10 hour flight for us in December.
Maybe I just didn't encounter any such performance when I was less... to be perfectly honest, I don't think I've ever seen a Shakespearean stage play I've been able to fully follow, even though my English is OK nowadays.
I've always had to use captions and backtrack/pause.
It might seem a bold assertion, but there's a reason that classically-trained Shakespearian actors are often cast in sci-fi shows (Patrick Stewart and Ian McKellen as perhaps the most famous examples). They're trained to convey more information through intonation and gesture so that you don't need to know the words they're saying, which translates well to performances in invented languages.