No. By this logic, giving any organization power is giving power to the people, because all organizations are "essentially groups of people". But that's clearly fallacious -- in all but the most bizarre cases, the local warlord's crime organization isn't nearly as representative of the will of the people as a democratically elected local government.
Companies are not democracies. Especially multi-national corporations and the lobbying arms of entire industries are in no sense representative of the will of the general public -- or even of their own employees (see unions)! This is significant because it is categorically not possible to actually choose not to interact with a particular corporation. In fact, the historical truth of that observation is the root cause of environmental, health, and many other regulations.
A defining characteristic of democracy is one person, one vote, and it is that characteristic that safeguards the will of the people. There is no corporate structure (other than unrepresentative radical experimental structures) that even conceits to affording one vote to each person. In fact, there's no provision of the TPP that requires the suing company to be publicly traded, so in some cases it may not even be possible to buy votes.
Your statement fails to represent the reality in that corporations are inherently undemocratic. They are groups of people controlled by a few people with all the money and therefore power.
Business's are amoral entities, designed with just a single charter: to increase the bottom line for it's majority stakeholders. Nothing about that is inherently democratic or good for their customers, for the environment, for the nation that company occupies, for anyone not in the company, or even for any one of their bottom tier employees by default. Any adoption of altruistic practices are either part of the companies branding and therefor good for business, or are core beliefs held by the majority stakeholders and are adopted by force. This also works for adoption of not so altruistic practices as well, and we shouldn't leave it up to chance.
If anything, corporate structure creates a multiplier effect on the influence of single humans or small groups of humans thereby corrupting the one-person one-vote intent of democracy. While I agree with the philosophical kernel of the Supreme Court's citizens united ruling that money is free speech, just like many things, at large scale, it has unintended side effects that need to be thwarted by campaign finance reform so that some people don't have MORE free speech then others.
Companies are absolute dictatorships generally owned by a very tiny class of wealthy elite capitalists. Calling them "groups of people" is deeply dishonest.
I see this as actually giving power back to the people.