Absolutely do not do that. First of all, it will not be quadraphonic, but four channel stereo which is a mess. More importantly it will blow up your integrated amp. That is because A & B speakers are not intended to be run at the same time. If you do then all speakers will be in parallel, and drop the load impedance low enough to blow your amp.
From what I remember of those speakers, and this is a long time ago, the bass was not well defined. Your ideal solution, but complicated, would be to put an electronic crossover in the preamp to amp loop and send the high pass to the JBLs and the low pass to the subs.
I am not really convinced that a cheap sub with no crossover is going to improve your listening experience and could make it worse.
Those JBL speakers actually go down pretty low. The issue is, that as I remember them the bass was far from the best quality.
As an historical note, your speakers go back to the old "West Coast/East coast" divide. JBL were East Coast and had the deeper 'tubbier" bass and Altec Lansing were the West Coast flag bearers with less deep bass, but tight as a drum literally.