Hello,
Thank you for the report. The logo and the layout have nothing to do with it: on your server, PHP loads zlib as a separate extension, and in that case PHP does not define the IMAGETYPE_SWC constant the new PDF engine of the plugin relies on since 5.0.0. So the error comes up as soon as an invoice is generated, whatever the settings.
We've fixed it in PDF invoice 5.1.1, which the plugin now defines itself when PHP leaves it out. Please download it from your account and install it over your current version, your settings and layouts are kept. It should fix the blank page.