But, is it really still bi-wired since I put that subwoofer in the path between the preamp and amplifier?
Bi-wire is running two sets of wires from one amp to one speaker. It really is still bi-wired.
Or did doing that essentially remove the bi-wire effects even though the speaker posts and speakers are still configured like a bi-wire system?
These are different questions. What is the effect of bi-wire? The idea is supposed to be that some frequencies travel better through one wire than another. This by the way is supposed to happen even when the two wires are the same. (It does.) So no you have not "removed" the bi-wire "effect".
Just as a matter of helping you think things through going forward, how would something done upstream ever possibly be able to remove the effect of something downstream that hasn't even been done yet?