Diego, thanks for the question. The issue is complicated, so I'll try to summarize point by point.
Ideally, they would want to have the community in a separate domain. This domain wouldn't have the logo of the brand. This community wouldn't promote the brand itself.
First off, I have to question the brand strategy. WHY does your company not want to the community to build the brand directly? A good, positive online community -- when run well -- can do wonders for a brand over the long term. Hey, just look at how much people love Moz just because of the community. I see no benefits to your company's idea -- and I see a lot of negatives.
The reasoning of this approach is to not interfere in the way of the community users and also the fact that the branded traffic acquired doesn't end up buying at the store
I don't buy this premise. There are times when direct sales are not the best Key Performance Indicator (KPI) of a certain marketing tactic. An online community builds a brand for the long term -- the KPIs may be metrics such as reach and more rather than direct sales resulting from community traffic and posts.
I'd read or watch this Whiteboard Friday -- it's on content marketing, but the idea is relevant. Few people see a piece of content and buy. But that's not the point. The more that people see the content time and time and time again, then the more likely it is that they will remember you when they do want to buy. It's the same idea in advertising: no one buys Coke because of an ad that they saw yesterday -- they buy Coke because of the ads they have seen for their entire lives. Likewise, no one is going to buy after reading a single community post. But the more that people engage and engage and engage with the branded community, the more likely it is that they will buy in the future. It's a long-term play.
Ideally, they would want to have the community in a separate domain.
Do you mean an entirely-separate root domain or a subdomain of the main root domain?
Either way, the same argument below applies.
I am concerned because the brand is not that big to have two domains separated and lose all the authority associated with one strong domain. I would definitely have everything under the same domain, store and community, otherwise we would have to acquire traffic for two domains.
You are correct. As much as Google likes to say that subdomains are treated the same as root domains, most of the data we've seen suggests otherwise. It's best to keep everything under the same root domain. If someone links to a community post or discussion and it's on a subdomain or another domain, then the main website will get little benefit.
Point: However, there are two times when a subdomain (or another root domain) may be better:
1. Creating a part of the website that will be less secure than the main website. Common example: A website has very confidential information, so they add a blog by putting Wordpress on a subdomain because Wordpress is less secure.
2. Very different design. It's a lot easier to have a completely-different design on a subdomain rather than in a subfolder on the main website.
Still, I'd suggest putting everything under the same root domain whenever possible. I hope this helps!