It's a good question if Facebook Page A Good Way To Promote MLM business. The answer is yes when done the right way.

But, you using it the wrong way will simply not work for you at all.
Have you seen a Facebook friends of yours in other MLM company flooding their timeline with series of posts asking anyone to join in his/her company? It may good for you at some point but to many people that are not yet open minded in MLM business can get annoyed.
Now, I am not telling you not to do it. What I'm trying to say is there's a better way how to market you business on social medias.
You may consider some of these reason why you should not make a Facebook page for your MLM company.
You need to make your OWN page to build your brand.
1.)Misrepresentation is one form of breaking the rule of the company. You could find yourself get blocked by your company and get removed being their distributor. You may take a look at your company policy because I am sure that it states there in the agreement.
Facebook also will not allow you to create a representation on behalf of your company without consent .
Here is what you can see on Facebook's terms of service before you can create a page.

"A Page for a brand, entity (place or organization), or public figure may be administered only by an authorized representative of that brand, entity (place or organization) or public figure (an “official Page”).

Unless you are really the representative of the company and and provide documents that Facebook is asking, you can get verified with blue badge or gray badge that's useful to gain more trust from your customers.
2.) You are not creating your own brand, if your page is name after the company, it's not you but your company name. You are not building your own name. Once you establish  the name of your page, you can use it more likely in the future so choose to have it your name.
3.) Your costumer can get confused. If they will searched your company name to Facebook, it will show a lot of pages with same company name.
4.)You will loose credibility when the company runs out of business. Given that you've gained thousands of likes and followers for your page, then it will be useless. Be very careful in choosing your company. I would suggest to choose the company that has built the credibility at least for 5 years. Start up companies has the highest risk to survive before it gone stable.
So, what are the things to remember in creating your Facebook page?

Build your brand 

Create your own name and start Giving value to people. Do not show people that you are too desperate to recruit people for your business. If you are after building your value, more people with like and trust you.
How to build Value for your prospects?
Its our next topic so make sure to keep visiting this blog for more tips.

Happy business day! Godspeed.