According to Zola's lines in The Winter Soldier, he was the one who began the HYDRA infiltration of SHIELD, and he wasn't brought in until after SHIELD was founded. So no, I don't expect to see any HYDRA infiltrators in Agent Carter. Nor do I understand why some people seem to want that. That's Agents of SHIELD's storyline. This is a different show and it should do something different, something new. And that's exactly what it has been doing by delving into Leviathan and the origins of the Black Widow program. It's adding something of its own to the tapestry rather than just telling us something we already knew.
There's certainly wiggle room here.
"After the war, S.H.I.E.L.D. was founded, and I was recruited. The new Hydra grew - a beautiful parasite inside S.H.I.E.L.D. For 70 years Hydra has been secretly feeding crisis--reaping war."
I agree it shouldn't be the main storyline of the show - just surprised it hasn't been eluded to at all. (yet)