Are the Cantonese word 係 and the Japanese word はい related?
The Japanese wiki page mentions that the claim is a "folk theory" that is "denied by academics". 

An alternative etymology for Cantonese hai6 comes from 系/繫. I don't have this book, but apparently Jerry Norman suggests this in Chinese (1988). This word had a very early meaning of 'to be connected', was used as a copula in later texts, and the phonological evidence is certainly not lacking. 

To summarize the wiki article, はい is thought to come from either 拝, a courteously used Sino-Japanese word, or a corruption of similar words such as "ai" and "ei". It is only attested from the Edo period onwards, which is very recent. 

Considering the relative isolation of Japan in the past few centuries, the word would have had to travel from Japan into rural Chinese villages in the past 100 years or so. Even if this did happen, it would likely have been heavily documented by various sources. The Chinese-internal etymology is much simpler and I personally see no reason to believe the Japanese etymology without further evidence.