I agree with Bob, especially if it's one set of frequencies that causes an issue (most likely if the sub is well designed). But it also wouldn't harm a sub to have it's port bunged, so as a 'what difference does it make and do I like it' test then it might be worth a quick go.
On the second question, answer is probably 'it depends'. The bass will roll off at a higher frequency (all else being equal). However, this could allow you to turn up the bass level overall, so actually giving a lower frequency response than you had before - AFAIK that's how the multi-ported subs like some of the SVS cylinders work, though they may also have different port lengths. Whether that helps with a boomy bass depends on why it's boomy. If it's a room resonance then it might if you are moving the cut-off above the boom frequency ... but, my guess is that it's won't unless you have a very large room. But, as noted earlier, it would only take moment to find out.
Greg