In short: no.
A bit longer answer:
Gnu Screen is only a text-mode window manager. It does not have the capability of actually making sure a process state is saved into disc and ability to restore it on next launch.
Such functionality is built into for example macOS, but given complexity of that even Windows operating system doesn't have that feature.
As a long-time fan of Gnu Screen, I have all the typical windows in my
.screenrc. Day-to-day life is handled by detach/resume, but when there is no detached Screen-session to resume, a new Gnu Screen session will always spawn my favorite apps into screens of my choosing.
# Genric settings
# Screen 0: mutt mailer (will alert on changes)
# Screen 1: bash shell
# Screen 9: Epic5 IRC-client
screen 9 nice epic5
# Go back to screen 0