Yeah, folks at my company follow discussions about our products on Twitter and it doesn't matter whether the person uses a hashtag or not. What you need is a distinct product name though, to only discover relevant tweets.
Hashtags make it easier, sometimes people don't provide enough context or use the same words you would for a product or service, if people start using a common hashtag it makes it a lot easier.
An example of this that I used a bit in my thesis (admittedly not product based) was the #ausvotes hashtag for the Australian elections. There were plenty of Tweets that would have been very hard to identify as related to the election without that hashtag because they were mostly thoughts or opinions without context.
