Can a band be considered heavy metal/heavy rock if they have a designated keyboard player in the group?

Deep Purple is regarded as a heavy metal/rock band.

Of course. Cradle of Filth, Nine Inch Nails, Dio, Alice Cooper, Dimmu Borgir, Type O Negative, Stratovarius, Ozzy Osbourne, Ghost...there are tons of metal acts out there with regular keyboardists.

It depends on which continent.  In North America, having a designated keyboardist is almost strictly forbidden for a metal band.  In Europe, it's pretty much required by law.  

You can have a member or two play keyboards in American metal occasionally (like Nikki Sixx or Eddie Van Halen), but you'll almost never find a straight keyboardist in the lineup.  In European bands there is always at least one keyboardist, and evidently they prefer a decidedly not-metal looking keyboard player.  Perfect examples would be Ramstein, Europe and this other band I can't remember the name of.  They're a Scandinavian power-metal act, lots of soaring vocals and wickedly galloping guitar riffs, and the keyboardist is this little short-haired geek with the glasses and turtleneck.

Heavy rock is a different story, and the piano / keyboard is much more accepted on both continents.  We're talking Rolling Stones, Meatloaf, Bryan Adams, Billy Idol, Loverboy, Steppenwolf, the list goes on forever.  

My initial response was no but then I thought what about the song 'jump' by Van Halen? That notoriously has a keyboard part in it doesn't it?

PS; Also, what about Europe with 'The Final Countdown'

Of course they can!

Heavy rock and heavy metal are NOT the same thing.  Iron Butterfly was very heavy rock and the organ was a key feature of their sound. Jon Lord and Deep Purple. Matthew Fisher and Procol Harum.  Almost the entire progressive rock oeuvre  featured keyboards - Yes, ELP etc...the list can go on and on.

Heavy metal eschewed the subtleties keyboards can add to the music in favor of extra guitars.

Of course; as other have already said, Deep Purple and J. Geils Band, and Iron Butterfly and Black Sabbath are two more of many. Black Sabbath had several, including arguably the best ever, Rick Wakeman.

Try telling that to Deep Purple, one of the greatest heavy rock bands ever!

Having a designated keyboard player doesn't mean that a band needs to incorporate keyboard parts into every song. King Diamond is heavy metal and the band has used keyboards from time to time, mostly harpsichord and organ, but not in every song. Just because a band happens to fall under a specific label, that doesn't mean that they can't write songs that don't fit that genre. Black Sabbath was as heavy as it was possible to be, but "Changes" wasn't a heavy metal song. So what? 

Type O Negative managed to pull off Harpsichord in a few songs.

Keyboards in several if I recall correctly.

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