Should language learners try to sound a little bit foreign?

In my last post I wrote about native speakers not knowing that language learners are not fluent.  I’ve experienced it many times when I have learned basic phrases in a language to be polite, and then have found myself apologising for not actually being able to speak the language.

So, is it beneficial for beginners to speak with a strong accent?  It gives the listener an instant clue that the speaker is not a native, and they can then (hopefully) modulate their language to suit the speaker’s level.  This saves you from having to explain that you are a student or that you don’t understand.

I’ve spoken to a few people about this, and opinions differ.  Speaking slowly or with a strong accent may benefit the learner in that the listener will modify their speech, but you can’t speak too haltingly, or ‘incorrectly’, or you may not be understood at all.  Most people don’t think that learners should actually try to speak with a strong accent (though some kind of accent is inevitable).

What do you think?