A group of English-speaking settlers travel to the Earth-like exoplanet of Rataan, which is 5 light years away. They board the generation ship Genesis that will reach Rataan in 200 years (0.25% of the speed of light). However, transmissions between Genesis and Earth are limited to text-only communications because of power costs. A new ship is built 150 years after reaching Rataan and reaches Earth in 50 years. Although the written form of English will likely remain the same over the 400 intermediate years, will sound shifts impair communication when the delegates from Rataan reach Earth 400 years later?
Absolutely. Look at how different American English and British English are after only 300 years, and that was with continual contact. Same with Australian English. A real, back woods Aussie is barely intelligible by the rest of the English speaking world. And just look at Scottish twitter. Unless your ship has some grammar nazis or English majors on it, the dialect will most certainly shift drastically in that amount of time. I'm sure they'd even come up with their own words and idioms and whatnot within 100 years. The dialect on Earth would have also changed drastically in that amount of time as well. Two diverging groups of the same language with no audible contact and written contact of status reports only? That'd be like taking a peasant from 1600s England and putting them in today's Louisiana Bayou. Communication would be difficult, but not impossible if the two groups cooperate to use words and an accent that they both can understand.
It can be an impediment if you want it to be. 400 years of linguistic drift within English is enough that linguists begin to treat it as a distinct language (Of course what is and isn't a distinct language is a fuzzy and ill defined distinction amongst linguists).
We can use this as a marker as a ballpark estimate for how much drift you can get in a 400 year span. It's enough that you can read documents and make some sense of them but not with the ease that you read the well written posts of this site.
Given that this is the amount of drift among one population and you have two to work with you have enough drift to have the populations as mutually intelligible as you like. One easy way to get the result you want is your decision about how effective their efforts to counteract this drift over the course of their voyage.
Yes, 100%, no verbal contact for 400 years is definitely enough for a language to cease being intelligible to those who speak the original (pre-isolation) form.
Look at Old French and Old Spanish, noir and negro respectively for the colour Black, and that is with linguistic contact. Being isolated would speed up the divergence. So yes, the span of four hundred years with no verbal contact would indeed leave them as classifiable as different languages from the verbal changes over time.
Another example to consider is the differences between Dutch and Afrikaans.
It evolved from the Dutch vernacular of Holland (Hollandic dialect) spoken by the Dutch settlers in South Africa
The Dutch East India Company established a colony in what is now Cape Town in the mid 1600s.
Until the early 20th Century Afrikaans was considered a dialect of Dutch but was later declared a distinct language.
Over time, different colonies of a language develop different terminologies based on what is important to them in their locality.
Pronunciations develop fashions, some die out and some continue, which can increase the divergence.