That is not how we usually talk. If you mean busy, try "我 máng 着呢。" or "我正 máng 。" Modal particle is a quite important part which makes your oral Chinese not awkward. And this character 忙 has a progressive tense in it(you are being busy). So annother keypoint is to put a 正 in front or a 着 after. If you mean blind, actually the most consise way to express it may be "我是 máng 人。" You can hardly say something serious by two syllables unless you are commanding someone.
That is actually a quite daily-used phrase. It means and only means 我很忙。 In Chinese, adjectives seldom show alone. Adverbs like 很 , 了(means something is done) or some modal particles always appear with adjectives. But 很 can not be used to modify 盲. Sounds not normal. Maybe, “我的视力状况很差。”
3.我 máng 了。
Like what I say in 1. This is too short for a serious statement when you mean you are blind. But it can actually be used when playing MMORPG and you suddenly go blind due to the ability of the enemy. So, that is something you will only say in a hurry. Well, most people may shout "我瞎了" instead of "我盲了" since 瞎 is more colloquial. So the occasion to apply "我盲了" may needs the debuff has a name refering to the character 盲 like “盲目” or “目盲”.
And 了 conflicts with 忙, since 了 means done and 忙 implies doing. Maybe, “我去忙了。”=you are ending the conversation and get busy doing something.
4.我是个 máng 人。
Ahha, just like what I said in 1. I omitted the quantifier to make it more condense but still practical. So, “我是盲人。”＆“我是个 máng 人。” are both authentic.
Well, actually, If you add a word, say “我是个大忙人。(I am a super busy man)”. It can mean self-mockery. The character 大 is necessary to emphasize the tone.
5.我是 máng 人。
So in conclusion, none of those 5 are ambiguous. Chinses language has some conventional structures to make sure you don't get confused in most daily case.
btw, 我忙 is not used. But 你忙 is often used when you know the one you are talking to has an important thing to do. And when that guy or you end the conversation, you say 你忙.
Literal translation is "you go and get your business done". But not in a commanding tone. It is actually a normal etiquette. With a little more respect, you can say 您忙.