Yes. The ONLY exception would be for any "opto" ESC. Those need an external power source, so you'd leave the red wire intact on those. But for any other ESC, no matter if its BEC is linear or switching, you'd remove the red wire.
Also note that programming certain ESCs might be problematic when removing the red wire. Some ESCs (like Castle's) use the throttle cable for programming, and the programmer adaptor powers the ESC when programming. If the red wire is removed, power is not getting to the ESC during programming. Just re-insert the red wire or plug the main batteries into the ESC for programming.
it says in the instructions to attach the red and black wires to the power wires to your esc. however, i don't want to void any warranties. can i just use a series connector to connect the bec to the esc and then to my battery? will it work the same that way or does it have to be soldered to the esc wires?