Are accepted papers going to be plagiarism checked?
In most of the open access journals, it takes less time to put the article online (one of the pros for choosing open access). It might take less than one month, even some cases, after paying the article processing charge, the journal put the author submitted version online. 

Now, for the conference paper, I guess the time difference between the acceptance date and actual conference date is not more than six months. In several cases, the author needs to upload the final camera ready version to the conference submission system in advance. If the conference maintains a good ethics, then the paper will be automatically verified with similarly checking softwares before sending the papers to the proceedings publication department — during this period, the open access article will be online. 

You get the idea on the consequences.