There are many ways for a computer to function and indent style is just one of those. There are so many innovations being done at the moment that it would seem as if functionality could be achieved in a lot of ways and there is more experimentation yet to be done.
Yes, I do think that indent style is necessary for computers to operate as well as they do today. Indent style is used to make the programs that run a computer, so it is an extremely important method that has been very useful in making computers run fast and correctly.
Right now with where we are at with technology and science I do believe we need the indent style for computers to function properly. I think that it is the system we have used for quite some time and we have not yet really branched away from it. Someday I am sure we will though.
Indent style is a practice built for human readers, not computers themselves. Indentation and white space make it much easier for humans to deal with text on screens, but computers have no such needs. Languages like Perl, where white space is arbitrary and up to the coder, function just as well as languages like Python, which does parse white space. The need for indentation also makes it necessary to use more complicated text editors to write in, as it's difficult to do by hand.
Yes, without indents a significant portion of the global population would probably go cross-eyed. There would undoubtedly be increased sales in aspirin due to a rampant epidemic in headaches. There would, no doubt, be a boon in medical specialists for eye strain. However, the computers themselves would continue to function just fine.