Given that γ (gamma) may have been pronounced as a voiced palatal fricative, it's perhaps not too much of a stretch to imagine that morphing into an unvoiced dental fricative.
Almost certainly not.
One of the discoveries that led to the creation of modern comparative linguistics was this: Germanic words starting with F tend to be cognate with Greek words starting with Π. Compare fire~πῦρ, feather~πτέρον, flat~πλατύς. This pattern is now known as (part of) Grimm's Law.
So the Greek cognates of "for" do not include γάρ, but a variety of short words starting with Π, such as παρά, περί, and πέρα, all eventually from Proto-Indo-European *p-r-.
(As a side note, Γ didn't become a fricative until post-Classical times, and English F is a labiodental fricative: the term "dental fricative" generally refers to the interdental fricative