Is there any way that a high-end fortune 500 company with the technological development of Google or Apple could successfully overthrow the U.S. government?
It's unlikely, but not impossible. After all, Hearst did manage to start a war, and that was 100 years ago.
Approach #1: Bully the vote
OK, we are shutting down GMail, Google Search, etc... unless you elect 100% the slate of leaders we want elected.
There are enough Google fankids or people desperately relying on Google infrastructure out there that they just might gain enough votes that way, especially of the slate they choose seems to be what 50% of electorate already likes but has hidden pro-Google agenda long term.
Approach #2: Buy their way in.
Some of the tactics to use (in conjunction):
Finance candidates they want
Finance attack ads and opposition research on candidates they dislike
Bribe candidates with money
Bribe candidates with policies if they already pretty much align ("hey, I know you care about urban housing. We'll invest $100M into building new urban housing and advertise it for free and advertise your policies for free, if you pass this set of laws we like. Small print: all the housing will have technology to redirect 100% of internet usage to Google Services. So we recoup what we did in 5 years in advertizing fees")
Approach #3: influence their way in.
They already do at small scale (lobbying). And major media companies already succeeded in helping elect US President they liked in 2008. And in the next 10 years Google and Apple may very well likely become far more of media powerhouses than they are today.
So electing people they want to positions of power is quite within realms of possibility.
Tweak their search algorithms to shape the information people see or don't see.
They already do that. They refuse to include "extremist" websites, which today they defined as "ISIS". They influenced searches for Brejvic (the guy who attacked kids in Norway). But there's no proof they will, or even have, limit themselves to ISIS in what they defined as "extremist". Tomorrow, it may be someone opposed to Net neutrality. Day after tomorrow, someone opposed to Google.
Publish content they want. 50% of youth in USA will vote the way Comedy Central humor hosts tell them to vote. Google can buy Comedy Central and make it their propaganda arm. Goal achieved.
... and once they have the candidates they hand selected elected, those candidates can pass any vote the company wants, amending the structure of the government.
The only missing piece is to appoint SCOTUS members who will interpret all that as fully constitutional. Not exactly a big stretch, considering how insurance companies managed to coopt SCOTUS in AMA situation.