Yes a person with visible genital warts may carry a high risk HPV type (HPV types that presist or progress could cause genital cancer) or he could carry a co-infection with a high risk HPV type…

The HPV test only screens for high risk HPV types and does not tell us what specific HPV type we carry. A biopsy of genital warts is not done to determine what HPV type or types a person carries. There is no way to know what type or types of HPV a person carries.

They are 40 genital HPV types.

How long a person shows visible genital warts is up to the person’s immune system….having genital warts should not affects this person’s ability to produce a child…many men and women with external genital warts have children.

HPV types 16, 18, 31, 33, and 35 are found occasionally in visible genital warts and have been associated with external genital (i.e., vulvar, penile, and anal) squamous intraepithelial neoplasia (i.e., squamous cell carcinoma in situ, bowenoid papulosis, Erythroplasia of Queyrat, or Bowen’s disease of the genitalia). These HPV types also have been associated with vaginal, anal, and CIN and anogenital and some head and neck squamous cell carcinomas. Patients who have visible genital warts are frequently infected simultaneously with multiple HPV types

http://www.cdc.gov/STD/treatment/2006/genital-warts.htm

Genital warts
Condylomata bearing HPV-6 or -11 have identical clinical
manifestations and histology [2]. Recent studies have shown that about
100% of GWs are caused by either HPV-6 or -11 but that 20–50% of
lesions also contain co-infections with HR HPV types [3] and [4].
Science direct

In effect, HPV is able to mimic our own chromosomes, behaving as a sort of ‘mini-chromosome’, independently replicating and keeping pace as the cellular chromosomes replicate and the cell divides,” says Tom Broker, PhD, professor of biochemistry and molecular genetics and co-author of the paper. “This allows the virus to remain in our bodies indefinitely, with the potential of causing serious disease years, even decades, after first exposure.”

****EDIT*****
I had much more to add to my post but since dates were challenged I thought I would supply you with these.

I will also point out that the link suggested is not a medical website…not monitored by anyone other than the bogus med it represents.

Dr. Broker’s information was accepted in 2006 at the International Papilloma Society meeting

More information is found at http://www.ipvsoc.org

Treatment possibly reduces, but does not eliminate, HPV infection

The CDC link was revised 2007

The information from Science Direct titled Genital warts was printed in 2006

HPV can be contracted from one partner, remain dormant, and then later be unknowingly transmitted to another sexual partner,

•When warts are gone, the virus is latent (sleeping) in the skin cells – it may or may not be contagious at this time
•Warts may appear within several weeks after sex with someone who has the wart-types of HPV, or it may take several months or years to appear. Or, warts may never appear. This makes it hard to know exactly when or from whom someone got the virus.

American Social Health Associations website was updated in 2009

Some HPV infections are thought to be suppressed and their genomes maintained in a long-term latent state (i.e., subclinical infection with a very small group of cells presumably maintaining infection at low DNA copy numbers). Support for a latent state for HPV infection comes from the observation that in some women genital warts can resolve spontaneously only to recur (i.e., reactivate) during pregnancy or when the immune system becomes compromised (e.g., HIV infection). It is not yet clear how commonly latency occurs in immunocompetent hosts, its ultimate duration, the circumstances and mechanisms that trigger re-emergence of HPV into a detectable state, whether latent HPV infection is ultimately eliminated in most individuals, or whether latent infection can persist, possibly leading to cervical cancer.
Natural History of HPV website was update in 2006

And with early disease one can be completely cured of cancer and continue to live more than 10years and may die of natural causes(as most of us will)