For certain printers (notably Brother multifunction) that are capable of borderless printing, LibreOffice does preserve the borderless setting and does not pass it on to the printer and it does not even preserve the setting between instances of setting the printer options.

For example:
File->Print, click Properties: Click Borderless, click ok.  Click Properties again and borderless has reverted to unchecked.

However:
File->Printer Settings, click Properties: Click Borderless, click ok.  Click Properties again and borderless remains checked, but then...
File->Print, click Properties: Borderless is again unchecked.

You can invoke the printer driver's config dialog infinite times through File->Printer Settings, and each time the "Borderless" option will have been preserved.  However as soon as you invoke it by File->Print, the borderless option is magically unchecked.

This is not the case in any other application.  Adobe Reader, Microsoft Word, even Wordpad all preserve the borderless setting in the printer dialog properly.

This is not the case with all printer drivers.  For example, Epson ESC/P-R printer drivers preserve and pass borderless to the printer and properly print borderless.