I assume by green card process you mean Adjustment of Status inside the U.S.? First, if the file I-485, the pending Extension of Status will be denied. To apply for B2 Extension of Status you have to prove they do not intend to immigrate during the extension period, which is obviously not true. The denial won't affect the I-485. They do not need to be in status to file I-485.
But a bigger problem is with potential misrepresentation. To apply for B2 Extension of Status, you have to attach a statement saying why their stay is temporary and what plans have been made for their return. If you then file for Adjustment of Status soon after that, it may seem like you lied on your Extension of Status application.
If by green card process you mean doing Consular Processing abroad, you can start by filing I-130 now. The Extension of Status may or may not still be denied because of this.