There are a few linux based IC CAD tools that can do some
portion of this but no idea about scripting vs GUI interface.
MAGIC has DRC and extract but LVS needs NETGEN or some
other (have found no other). layouteditor appears fully
featured but costs $$$$ if you want the verification tools.
Cadence of course runs under linux but now you're talking
$$$$$ - $$$$$$. Some other tools sets are out there but
you're likely to find yourself lonesome and "80% of the
way there".
In any case this "turnkey verification" has value only once
all of the hard work has been done, by the usual mix of
manual and scripted time and motion. What happens with
found errors? Back to GUI. How do you get the schematic
and layout DBs in the first place? Back to GUI. And by the
way, schematics are not GDS-II format (at least, have not
ever seen a schematic stored in that way) and there is
no real schematic data format other than EDIF, which is
seldom if ever fully functional and would need its own
netlisting to a LVS-recognized format.
Possible? Yes, just add effort (substantial, and expect
only partial "coverage" of the tools sets / formats in
play.
Practical? Well, how much spare time and skillz have
you got?
Marketable? Not likely, integrating one-trick point tools
is not a popular activity with corporate CAD
decision-maker$.