I could see this having an effect on the ongoing
development of each language in a way that might leave
them closer together than they would otherwise be.
For instance, if I take my previous example further, if such a situation existed with English and German, the words "wit" and "thou" might have ended up being more common in spoken English, or at least considered more formal rather than archaic. Certain grammatical constructions might also end up being more common, such as the continued use of the y- prefix in past participles.
I'm already stretching this analogy more that I should, but hopefully it gives a better idea of the relationship between Cantonese and Mandarin.
Many Mandarin speakers see Mandarin as being equal to "the Chinese language" and often think of Cantonese as being "merely a dialect" of Mandarin because Cantonese speakers appear to read and write the way they do (even though the aforementioned examples show that this is really not the case), and they are not really exposed to the more major differences that would exist if Cantonese speakers actually wrote the way they spoke.
Cantonese speakers are more aware that they don't write the way they speak, but because the Chinese writing system only reflects the lexical and grammatical differences rather than the pronunciation differences (even though most of the differences are in the latter), many Cantonese speakers end up considering the written language as being a "formal" version of their language rather than a different language altogether. For this reason, many Cantonese speakers also consider Cantonese to be a dialect as well; however, they consider both Cantonese and Mandarin to be dialects of "Chinese" rather than Cantonese being a dialect of Mandarin.
Linguistically speaking, because spoken Cantonese and Mandarin are generally completely unintelligible to each other, they should be considered separate languages, but the the writing system ends up obscuring these differences. There are also political implications if Cantonese were considered a separate language because of Chinese nationalism tends to see that as a slippery slope towards separatism.
While I think (second hand - I have no deep familiarity with either language) that your broader point holds, this particular bit is weaker than it might be read. While the split happened longer ago, there are more day-to-day attempts to communicate between native speakers of Cantonese and Mandarin than between native speakers of Modern and Shakespearean English. I could see this having an effect on the ongoing development of each language in a way that might leave them closer together than they would otherwise be. (Shakespearean English probably does have some continuing impact on Modern English, but I think we can be fairly confident that there's no influence the other way).