Yes, companies such as Google, Apple, Microsoft, and Facebook hire students from BITS, VIT, or KIIT. In fact, they hire from colleges all across the country. These companies are all for skills. If you have the required skill set, you can get interview calls from these companies. If you belong to some IIT, you will certainly have some advantage over the others.
You are in for a treat because they definitely hire from BITS, KIIT and VIT. My cousin studied CS in VIT in 2018 and now he works with Facebook with a really great pay scale.
You should not be concerned about this because they hire from any college in India, be it in the top 20s or 200s if you have the requisite skills they are seeking. These well-known tech brands you mentioned, are all in for professional skills.
If you are an IITian, then you do have an upper hand, because everyone in India at least, is overly familiar with the brand which IIT is. However, don't expect any special treatment just because you've got what it takes to crack interviews.