Fast: No, not even close. Most of the v-tec'd Civics around here are the eco, or inverse version of the v-tec, making their ricing out a bit ironic, really.
Common Mod: [censored] cannon, HID lights, rims (rear, then front, as they can afford them.)
EDIT: Could a good driver in an appropriately-modified Civic si beat me around an auto-x course? Absolutely.
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Some small "ricers," such as the CRX, are actually designed like little gokarts and really do handle pretty well. Fast, still a big, fat no.