The short answer is a resounding YES. Even if you are referred to a company, you are highly likely to need to complete some sort of application online.
The good news is that most applications can be completed on a mobile device, like a phone, so having access to a computer is less of a complication these days. At the same time, access to technology is a real barrier for some and we collectively don’t yet have a good solution for that, beyond the common advice to “visit a library or workforce development center.”
It is also highly likely that you will need an email address in order to communicate with prospective employers. If you set up an email address just for the purpose of applying for jobs, be sure to monitor your inbox and SPAM folders. This will be the first mode of communication for most organizations that are hiring.
Most online employment applications can be completed in less than 30 minutes. In the end, this is much less time than you would spend driving to each company and filling out a paper application onsite.