Live website moving to localhost

Hello,
On my live website I have a problem, which seems to be coused by a plugin. The plugin support adviced me to run a debugging process. It can not be made on live website, it is not recommanded, so I would like to make it on localhost with the newest backup version. I use xampp for localhost.
Could you tell me, please, what will happen with my original website, if I use Migrate DB plugin to rebuild my site on localhost? Will it affect my live website, when something will going wrong on the rebuilded page on localhost?
The two site will have the same database?
Thank you in advance for your help,
Best regards, Maria

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