Not likely. Every time communications technology takes a step forward, linguistic drift is slowed down. Star League Standard English is probably intelligible to a modern speaker thanks to audio recordings and such helping to keep words pronounced the same way, like how the printing press put Middle English writing in a bodybag. There'd likely be a ton of newly invented words and loanwords, but a modern day speaker with a 31st century dictionary could probably have a conversation with a ComStar adept.
Of course, given the whole fall of the League bit and the ensuing collapse of technology, chances of understanding someone from a backwater Davion planet are anyone's guess.
they Used to think this, 50 years ago. that Radio & TV would slow linguistic drift.
In fact, it hasn't slowed it down one bit. The Great Northern Cities Vowel Shift happened in the 1960s, as dramatic a shift as the "Great Vowel Shift" in the 1400s in England.
Linguists now think there will be a 'Southern' English, a 'Northern' English, a 'Western' English all in the current US territory in 500 years or so. About as mutually intelligible as, say, Spanish, French, and Italian are to each other today.