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.
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.