There are legal issues, however in most states I believe this would be legal. You would almost certainly need to draft some terms and conditions, and you would probably need an alternate means of entry for people who cannot tweet...
But overall because Twitter is free and publicly available and there are no direct barriers to entry it should be possible.
I am not a lawyer. Read the laws yourself, and consult a lawyer if you have any doubts.
This community isn't the right place for this question. You need to consult an attorney. The laws vary from state to state, but in California, I'm sure you'd have a legal issue here.
I'm also skeptical of the success of such an approach on Twitter, but you didn't ask about that, so...
The part about legality has probably been sufficiently answered, but on using Twitter.
I think it really depends on your industry, for example, if you have a lot of ideas, then you can share some over Twitter, and then go into more detail on your tech blog, so that if people are interested in one of your random thoughts (At restaurant thought it would be great to give reviews online :), then by going to your blog they can get a better idea about what you know, and your willingness to share ideas because you are overflowing with them.
This way you are not just talking about yourself, and you may get some followers that would typically not follow you, esp if your ideas are really creative and sufficiently different.
I think using Twitter to directly draw business would turn a lot of followers off, as it is too self-serving without really giving back to them, but sharing book plots, movie plots, song ideas, as well as ideas for new programs would be a draw.