Nope, you shouldn't need a c-section. Just make sure you're prescribed the cream for it and treat it throughout your pregnancy if you have visible warts, especially in the weeks leading up to when you're due if you notice any.
HPV (the virus that causes genital warts, cervical cancer and cervical cell changes) is one of the most common infections. Most people have been exposed to it or are currently infected. It's almost impossible not to get if you're sexually active for long enough as using a condom won't prevent it (it's spread entirely by skin to skin contact, not body fluids, so you don't technically even need to have penetrative sex to get it). 80-90% of adults in Western countries will become infected during their lifetimes and it usually clears itself out within 1-2 years. You might find yours disappears too before your baby is even born. But it doesn't mean you automatically need a c-section unless there is some other serious complication. I have a history of abnormal cell changes on my cervix (have had it biopsied, etc.) so I very likely have it myself. It's so common they don't even test for it in most people with cervical problems as nearly all women in their 20s and 30s have it or have had it recently (though most will never know it). I didn't need a c-section (and in fact, no one even asked about HPV knowing about my history with cervical abnormalities). I had a natural birth at home and my daughter is perfectly healthy.
So make sure you treat the visible warts now, but you shouldn't be pressured into a c-section unnecessarily.