Yeah, you can cut off the stock speaker plug and use the oem wiring, just make sure you get your positive's and negative's straight. If you get one backwards you'll get phase cancellation with the other speakers, it'll make the bass disappear mainly.
Or you can run your own speaker wire through the doors and to the radio (called "hardwiring"), but I can tell you now that it's a pain in the ass the get wires into Integra doors through the stock boot. If you running just entry level speakers, just use the oem speaker wiring and save yourself the trouble hardwiring.