I answered this in Mandarin first. I didn't realize that happyrabbit hoped the answer could be in English until I submitted it, so I'll post the English version now.
Yes, 刺激 has the meaning of exciting too.
But if I want to be hair-splitting, the 了 in 我看的足球比赛很刺激了 is not needed. Just say 我看的足球比赛很刺激 and it will do the job. To make an exclamation, you can say 我看的足球比赛『太』刺激了.
I know that 了 can have the sense of affirmation, but it seems to me that it's not common for 很 to have 了 tagged along. It's probably because the character 很 is already an affirmation; therefore, we don't necessarily need the help of 了 to make the tone complete. For example, we say 我很忙,别来烦我. It would be a bit odd if you add a 了 and make it 我很忙了. However, putting in 已經 and saying 我已经很忙了 makes a good flow.
In addition, when 了 is used after 很, it seems like (I'm not a professional Mandarin teacher so I'm not sure of this) this 了 means a twist (, which means what comes next is what counts), and 已经 is very often used as well. For example: 他 (已经) 跑得很快了,可是还是输了. It's equally good to add 已经 to the front of 很快.
As a result, when I saw 我看的足球比赛很刺激了, I was like, "And what happened next? Anything else more exciting?"
太 is very often an extreme affirmation (or negation), or an exclamation, so it almost always has a 了 tagged along.
You in fact asked about 刺激 but my answer turned out to be talking about the usage of 了. What a digression (the Mandarin internet lingo would be 楼歪得很严重). Sorry about that!
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To Cherry,
What you said is very true, but 刺激 does sometimes means exciting. We use it a lot to refer to anything exciting, or anything that can turn you on.