First, that's a mighty big if, and second, it's not enough!
Voting is a process where unlike online banking or online shopping there is no way for a human to go in and fix errors, there's no way to audit a vote and go "Oh, Bob meant to vote for A and Cindy meant to vote for B, so the machine did it wrong". It's not enough that an electronic voting system is correct, every single voter has to be able to trust the system, and for that it needs to be simple to understand.
You can't look at the electrons inside a silicon chip to determine they're doing the right thing. But with pen and paper and envelopes and urns and observers and counters, you can determine that the system is doing the right thing. Involving lots and lots of citizens in the voting system is not a bad thing, quite the opposite! You want as many eyes as possible on the entire process to ensure there's nothing shady going on, that there's no mistakes.
But if all the votes go into a black box that spits out the results, all of that goes away, all of that trust, all of that ability to verify that the results are correct.
Somehow you have gone from one extreme (implying that a traditional paper voting system is always trustworthy) to another extreme (saying that all voting systems can be corrupted), which, by the way, is not true either. For example, the results of a voting system where all votes are public, can not be manipulated. This tiny example shows that clearly some voting systems can defend against corruption.
They'd have to give each voter some sort of voting device with a screen, buttons and wireless connectivity, and make sure that the voter doesn't lose it so that it can be reused for the next election, or buy these devices each election. Too much trouble.