Yes, you will be able to re-download but you're only allowed to so many copies (unsure how many). If you need to re-download you need to de-authorize the old computer first: https://help.ea.com/article/using-the-de-authorization-tool-for-the-sims-3
I do think you can contact Customer Support if you run out though. I'm not 100% sure how it works cause I only use DVDs.
Maybe someone else has some more experience.
You could also contact Customer Support. I would think that is a question the should be capable of answering.
They can be found here: https://help.ea.com/contact-us
Choose a category, a game and a platform for the option so show up.
If live chat is gray, change your country to US and make sure you're on US Business hours. It might also gray because they're very busy. Try later.
See this post if you have trouble with the site: http://sims3.crinrict.com/en/2012/10/how-to-contact-ea.html
