Yes, unlimited corporate spending upholds free speech, because there is no way to limit corporate spending on lobbying and other speech issues without violating the First Amendment. The First Amendment is quite clear that there can be no law abridging freedom of speech. The Supreme Court has constructed very limited exceptions to this Amendment, and it would be unfair to limit the rights of only certain groups, in this case corporations. Each person or entity should be allowed to influence politics as much as they are able, with the resources they have.
Unlimited corporate spending on political campaigns doesn't uphold free speech. If speech is free, why are businesses allowed to spend unlimited cash on politics? That means campaigns can be bought and are far from free. Campaign spending should be limited so individual Americans have more choices in politics on any level of government.