Yes, they will! 

Once there is a new review available on the Google My Business listing, it will be picked up by Review Pops automatically after it's available through Google API (usually within 72 hours). 

That review will then automatically be displayed in the Review Pops banner on the website.  Moreover, if you need to make any adjustments to the style or color scheme of your review pop, edits will automatically be available on the website without the need to manually update the code on the website.