... I had so much written in here, then just clicked back on accident... <sigh>Let me start over...</sigh>
Unique content will help gain followers. The more followers you have, the more FB shares and likes you "should" have. This is where FB pages can impact how your website ranks in Google's SERPs.
The biggest thing with FB pages is that they need to be monitored to interact with followers, responding to their questions and concerns, and updating your content. If you do not do these things, you will not get the followers, shares, and likes you are wanting.
Depending on your company, Twitter, LinkedIn, or Google+ might be a better form of social media; however, like FB, they still need to be monitored and followers will demand interaction.
As for increasing your DA... it is wicked tough to do in a short period of time. According to SEOMoz:
"How do I influence this metric?
Unlike other SEO metrics, Domain Authority is difficult to directly influence. This is because it is made up of an aggregate of metrics (mozRank, mozTrust, link profile, etc...) that each have an impact on this score. This was done intentionally because this metric is meant to approximate how competitive a given site is in Google.com. Since, Google.com takes into account a lot of factors, a metric that tries to calculate it must incorporate a lot of factors as well.
This means the best way to influence this metric is to improve your overall SEO. Particularly you should focus on your link profile (which influences mozRank and mozTrust) by getting more links from other well linked to pages."
The short of it is that if your SEO provider is creating multiple FB accounts and they are having issues with maintaining multiple accounts, you are definitely better of with just using one. If they put the amount of time and resources into managing one account over multiple, in theory, you should be able to accumulate more followers, likes, etc., because you will be creating unique content for one source instead of creating thin content, you will be providing great interactions with followers, instead of responding a few days later, etc.
Does that help?
Mike