Can the 1st generation Grubbs Catalyst be used for ring closing metathesis on non-terminal alkenes?
Yes, it appears that that ring closing metathesis of non-terminal alkenes has been performed using the 1st generation Grubbs catalyst several times:


Asymmetric syntheses of enantiopure C(5)-substituted transpentacins
via diastereoselective Ireland–Claisen rearrangements
Stereoselective Synthesis of Deuterium-Labeled (2S)-Cyclohexenyl
Alanines, Biosynthetic Intermediates of Cinnabaramide
Ru-catalyzed metathesis of octadienylether xyloside Synthesis
of (−)-Agelastatin A by [3.3] Sigmatropic Rearrangement of Allyl
Cyanate
A chiral auxiliary cleavable by ring-closing alkene
metathesis — Efficient synthesis of chiral nonracemic
cycloalkenes
Conversion of chiral unsaturated cyanohydrins into
chiral carba- and heterocycles via ring-closing metathesis
Total Synthesis of Pancratistatin Relying on the [3,3]-Sigmatropic
Rearrangement
Stereoselective Chelate-Controlled Addition of Grignard Reagents to Unsaturated Medium-Ring Heterocycles