Can I send an updated version of my resume after I've applied?
No. Not unless you really screwed up the first time. When it comes to a job application you typically only get one shot at passing along your resume. Application deadlines are usually long enough that you have more than enough time to write a cover letter and rework your resume and as such you're expected to get it right the first time. If you only saw the job ad right before the deadline that's typically a mitigating factor but even then you'd only send in an update if the original had significant problems.
If you're only making minor changes like fixing a typo, adjusting the layout or rephrasing some bullet points then any benefit those changes would have would be more than cancelled out by calling attention to the fact that you didn't do this before you applied. Attention to detail is important in virtually every job and sending or uploading an updated version of your application is basically saying "I wasn't careful enough the first time". You need to keep in mind that if you're making these kinds of changes, you're going to have to be able to answer the question of why you felt the need to send a new version. "I didn't like the formatting" won't cut it as a valid reason.
For minor stuff you should just put it out of your mind and hope that they either won't notice or that they'll want to talk to you anyway. If you're a good fit for the job, minor resume nitpicks will never get in your way of an interview.
Now if you're talking about major issues like using a resume that's two years old, of course, you should send in the correct version because of the damage that mistake could do. Using an old resume will harm your chances much more than simply admitting and correcting mistake. Only draconian managers will refuse to consider you over a mistake since you're only human, but it's usually better to avoid drawing attention. If you sent in a resume that you customised for a different position so that you left off highly relevant information, you're going to have to make a judgement call regarding how much of a difference it could make.
If it's a major error that can't be mitigated, like using the wrong company name in your application, you'll simply have to hope they either don't notice or will forgive you for it.
The fact that you applied online ultimately doesn't really change this. You indeed have no way of knowing whether they already grabbed your old version or whether they'll be notified so you'd have to contact them if you wanted to make sure. Again: only something you'd do for major errors.
What I would do is to print out both versions of your resume and bring those along to an interview if they invite you to one.