The reasoning behind this argument, for those who are unaware, is that the decline of freeholding citizen-soldier-farmers from the days of the Republic led to a decline in the Roman democracy, and eventually, to the Empire as 'barbarians' took over the ranks of the soldiery and undermined the 'Romanness' of the state. This is the classic argument Gibbon makes in the Decline and Fall, and it generally blames Germans, Christians, and rich slave-owners destroying the economy and army.

Modern historiography has moved away from this interpretation of both the economic and social causes of the fall of Rome, and instead tended to focus on the political. Peter Heather, one of those who is one of the staunchest critics of the Gibbon storyline, suggests that it was a combination of the rise of Persia, amalgamated Germanic tribes, and weak domestic political structures within Rome itself that helped lead to the 'fall'. He makes some very compelling arguments that suggest economically, although weakened thanks to a variety of factors, Rome still was chugging along in the 4th century relatively well considering all the turmoil, plagues, and contraction it had experienced in the prior century or so, but basically from around the 360s onward experienced a marked and rapid decline.

I'd say most classicists tend to, like Heather, look for other rationale to explain this rather than blaming the Christians or Germans, whom, after all, had formed important parts of society for at least a few generations before the Empire really started to come apart. I don't see any particular reason why unequal wealth distribution need play a large role in that given that the Empire existed for a very long time with pretty much the same uneven distribution for most of it's final centuries.