Here are a few important limitations you should be aware of:
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The search results provided by Twitter are often incomplete--you will most likely NOT get all recent tweets that match your search query. The way Twitter puts it is that the results are "focused on relevance and not completeness."
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Twitter will not provide NodeXL with tweets older than about a week. It is NOT possible to use NodeXL to get tweets older than that.
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The algorithm that Twitter uses to match tweets with a search query is undocumented. It is NOT, however, the same algorithm that Twitter uses on its own search page, so you may get results from NodeXL that differ from what you get directly from Twitter using the same search query.