"Does the accent really matter?" is the correct version of your question. To answer, I would say mostly "yes"; If a foreigner from a non-English-speaking country has a very strong accent, he or she will likely be difficult to understand. Foreigners without enough English (or practice) still speak using the same tones/inflections/accents that they use in their native language. Essentially, they're speaking English as they would speak their native language, and that's not the right way to do it. :) That leads to confusion and lack of comprehension to the receiver of your speech. That's partially why it's important to learn an accent of the language you're learning.

Accents don't matter, as long as people can understand you, but pronunciation is important.

I think, in reality, it is almost impossible for a secondary language learner to speak as exactly as the native speaker of the language he or she is learning. Even living abroad for years. And I think it is cute if you're speaking with a little accent, on the basis that you can make others understand you perfectly well. You're not American right? I don't think they expect you to speak standard American English. No offence, from my personal experience, I find some middle aged Singaporean people's English difficult. So I need to work on that. However, I aim to understand people all, no matter which kind of accent he or she is carrying. I personally prefer British accent, so gentleman. :)

When we are learning and practicing a second language accent is really important but, believe me, you will not speak as a native speaker if you are not a native speaker. You can pronounce very similar if you have enough practice but, instead of worrying about accent it would be more important to know new vocabulary or phrases to use them in real conversations and to know the differences about meaning between countries of English speaking for example.

How can anyone say accents are important! Take England for example, there's a basic english one which most foreigners will hear as similar. Then there's the main north and south differences. Then within the South there's a general one, a posh one, cockney, bristol and west country. Then in the north there's lancashire, yorkshire, tyne etc. Then within these there are even more! Like Scouse, Mancunian, Geordie. Then within places like Greater Manchester you can tell differences between Salford, bolton and Oldham etc. I think pronunciation is important, but I think learning an accent is a slight waste of time. Many English accents arn't understood in America, new zealand accents in Australia etc etc. From my own experience, It would be best to learn the accent for where ever you live. Because not only is the accent different but many words will be too, for instance..... thongs, jandels and flipflops are all the same item, just different words used to name it in different countries. If an Australian went to England and said they are wearing thongs, a pair of rubber sandles wouldn't spring to mind.......