No. That is not currently even an option.
@Skalman has the right answer: Jumpdrive.
So, with the right boot incantation, you connect your Librem 5 to a Linux host via USB and boot the Librem 5 over USB - and the software to load over USB is Jumpdrive. Once Jumpdrive is booted on the Librem 5 it exposes your eMMC drive (and the uSD card if present) as USB disks (block devices) to the Linux host. With that done, you mount the eMMC drive on the Linux host and then you can fix up the sudoers file or most other files on the Librem 5’s eMMC drive.
(The procedure is basically the same as reflashing except the software that you boot over USB is different. Either way, it can get you out of tight spot if the content of the eMMC drive is stuffed up. The difference is of course that reflashing nukes everything, so sooner or later you are going to want to try Jumpdrive, if you are a bit of a tinkerer.)
I think your problem is that the root account is by default disabled (expired and/or locked) on most distros in the Debian family. Refer: Expired root account
There are some reasons to keep the root account disabled.
That in and of itself sounds like a good idea. You can have a stronger password for the lockscreen but that could be quite tedious. You can also prevent purism from doing sudo at all (and do all your sudo work from a different user) but that would surely cause other problems.