Can businesses survive today without using social media?

Not always, depends on the area in which you do business.

It is all about these two concepts:
1- Segmentation.
2- IMC Integrated Marketing Communication If the Segment you are targeting is not available on the Internet in general then why to use social media? Also if it was available, but by siting the overall strategy you have found it is more suitable to use other channels than social media, so why to use it? Yes the business can easily survive without social media only if rule1 or2 apply.

These days companies can not compete without the use of social media

The promotion channels can be chosen after identifying the product and the targeted segments of the market; these elements decide whether social media promotion is necessary for the business survival or not.
But the fact is that the social media is playing a remarkable role in creating awareness.

Yes, but not all type of BUSINESS.
I.E.
Pharmaceutical industries.........etc

It truly depends on the type of business however: Social media keeps followers engaged, up to date and gives them the feeling that they are apart of the business -"in the know", as well as giving them an insiders view that people who don't follow them don't get.
Those really interested will find the constant update from the companies they follow as key to their enjoyment to the products and projects the company has.
It is the future, and many companies from drink brands - Coca Cola, to sport products - Nike and even travel companies - Virgin, are getting involved.
I'm positive that in a few years most companies no matter how small their online presence is, will have some sort of social media.

Surviving any business is by establishing a solid infrastructure, through a qualified section heads, and organised sections synchronising and developing the work flow simultaneously, social media is part of, and not the main anchor for the success.

Yes sure any business can survive without using social media.
But it won't move to the front end if the competitors are going all live.

Business relating to social Media can survived only through the social Media, and can collapse without it.
Eg advertising a media chat applications, computer and mobile phones walpapers, computer applications, etc.
But other businesses that is not relating to social media, uses social media only for advertisements, hence can not collapse without it.

Yes, they can survive without using social media.
Will they be as successful as they need to be that is another question altogether.
As an entrepreneur you want to do more than just survive.
With that in mind you want to be versatile in your approach to the market.
The idea is to always try to expand your market base.
A good deal of today's market uses social media.
So you want to expand your approach to meet that market base if you want to increase your probability of success.

social media is nothing but connecting professional people online and directing about our products, it can be worthy but not for surviving.