Are megabytes deducted from your Verizon data plan on a Driod if... (Best answer?)?

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If you buy a Droid smartphone from Verizon using a limited internet data plan, (the $15 one), does it deduct memory from that plan to use an application that runs using wifi? (i.e., would it cost megabytes?)

Thanks in advance!
Oops, so sorry, I mean on the 3g network, not wifi. Would it count toward your memory to use an internet-based application on a Droid?? Sorry and thanks..