Which model do you mean when you say "original" Roku? There have been about a dozen earlier models. Look at the comparison chart on the product page to see the differences between the LT, Roku1, Roku2 and Roku3 models.
I don't think the answer to your question is "no". The answer is "sometimes". I know of no way to live stream any of the major broadcast networks via Roku. However, there are many ways to access network shows, particularly prime time shows, as soon as the day after they air. Some of those ways involve a subscription (Hulu Plus is the best example of that since it has the widest selection of current shows) and some do NOT involve a separate subscription. For instance, through my free Plex server I can select a wide number of what Plex calls "Channels", including some of the major networks plus AMC, Bravo, History, etc. Through that access I can watch many current shows that are available from those networks on demand. For instance, right now on the CBS "Channel" I get through my Plex server I can watch the latest 3-5 episodes of just about every show that airs on CBS. I assume that this same content would be available to me via computer from CBS.com but this way I'll watch the shows full-screen on my HDTV in what for me is very high resolution. This is one of the beauties of Roku -- in many way it allows you to get content you could get on your computer but access it through easy navigation controls and watch it on your big screen TV.
Even though the total number of "current" shows that you can watch one way or another through Roku might be quite large, though, the process will probably continue to be awkward and what you can get will continue to be hit or miss.