This comes down to editorial practice and whether it's being used as a proper name or not.
So in Caesar's Gallic War, Seel capitalized both Cisalpina and Gallia, because it's Cisalpina Gallia, one place (my edition by Du Pontet has the same):
uos ex Cisalpina Gallia consulis sacramento rogasset
However, Rossbach left the C uncapitalized in his edition of the Periochae (same with the unknown TLL text and the presumably Paul Jal's Bude, but I don't have access to the latter at the moment):
M. Brutus, qui cisalpinam Galliam optinebat, a Cn. Pompeio occisus est.
When it's not used as a proper name, though, it seems to be uniformly uncapitalized, like with pergraecari. These all were taken from PHI:
Titus Maccius Plautus, Bacchides 813
Nic. Propterea hoc facio, ut suadeas gnato meo
ut pergraecetur tecum, tervenefice.
Chrys. O stulte, stulte, nescis nunc venire te;
Titus Maccius Plautus, Mostellaria 22, 64
corrumpe erilem ádulescentem óptumum;
dies noctesque bibite, pergraecamini,
amicas emite liberate, pascite
date, si non estis. agite, porro pergite
quoniam occepistis: bibite, pergraecamini,
este, ecfercite vos, saginam caedite.
Titus Maccius Plautus, Poenulus 603
liberum ut commostraremus tibi locum et voluptarium,
ubi ames, potes, pergraecere. Coll. Eu, edepol mortales malos.
Agor. Ego enim docui. Mil. Quis te porro? Coll. Agite intro abite, Agorastocles,
Marcus Cornelius Fronto, fragmenta 12.1
parentum tuorum.
Et pergraecari potius amoenis locis quam coerceri carcere
viderentur.
Pergraecari is a verb meaning "to live like a Greek" (i.e. playfully, so "to revel"), whose root is Graecus, a proper adjective.
Based on this, I'd say put it in lower-case unless used as a substantive.