In Self-Improvement, in large, the consensus is that Money is a means to an end.

Those who use their money now to be happier, will be happier with more. As more money will buy them more extravagant experiences and more of them.

Those that cannot use their money for happiness now, fall into two categories:

Those that do not have enough to spare (These would fall into the category you mentioned, and would likely get happier up to a certain, comfortable amount), and those that can spend some money, but do not spend it in ways that actually make them happy (as an example: they buy brand articles that are just for show and do not create any real happiness; these people do not get happier with more).

The short version is: Money only increases what is already there. Meaning that if you can be happy first and then come to money, you will exponentially increase that happiness (similar to when people talk about relationships).

That is the current standpoint, and a very generalized opinion, and will absolutely differ from person to person.