New logic board

The usual Apple policy is three repairs to the same component before they will consider replacing. Otherwise they just fix whatever is wrong.

 

Since nothing has been done, then no, they will not replace your MBP. If you have had several repairs and the computer has been out of your usage for extended periods due to problems, then they may replace it at their discretion. Since you have had neither of these, through the AppleCare, you are obligated to let them at least try and repair the MBP. If you have had logs that prove your errors and they can't repair the issue(s) (and this is assuming actual issues exist), then they may replace at their discretion.
Remember, if the issues are due to a third party add-in or program, they are under no obligation to replace nor guarantee compatibility and these issues would be considered non-issues, as log as the basic functions of the computer as designed and shipped work correctly (I know this sucks, but it is what it is).

 

I also have a 2010 MBP and just last week had to have the logic board replaced. I will say that once the problem was correctly diagnosed, the repair took less than 24 hours and the MBP works flawlessly...