Nah, from what I remember of the source(the modding SDK exposed a lot of the engine internals) it was a mix of Q1 + Q2(I think the Q2 part was mostly networking code).
Keep in mind there was Hammer(the level editing tool) which grew into it's own thing as well.
It was a Quake 1 / QuakeWorld mod... I remember playing it via GLQuake, only time I ever played a game more than two days in a row... played so much over that first weekend-week, my muscle memory reset, at work my hands didn't go to the home-row keys on the keyboard for a week.
My understanding was that the first Half-Life essentially was just a Quake mod. Amazing stuff.