American elections can only be influenced by foreigners if non-citizens are allowed to vote. Corporations don't own elections even though they try to buy votes with billions spent on commercials and campaigns. Unlimited spending didn't help Mitt Romney in 2012 and it won't help in the coming elections either. The Supreme Court controversy in favor of the GOP was, thankfully, proven wrong when companies were allowed to spend as much as they want towards political causes.
No, unlimited spending in corporate free speech cannot avoid foreign influence, because there is a lot of money to be made in U.S. politics. Many foreign people and countries have an interest in U.S. elections, and they will use influence from corporations in order to try to influence elections in the United States.