In my place citations do not count towards your final word count. Technically they're not your words, so why count them? This is to say nothing of the pain of adding up all your citations, but even if you get a rough count of what you're citing you can be more liberal with your overall estimate of how many words the paper actually is.
I have to quote large sections of newspaper columns and several stanzas of poems etc, if this counted towards my final word count, I'd never get to say anything. So no, I don't think it's cheeky in the slightest!
Best of luck.;-)