Yes. You can use the marine rig on the ham bands, if you have a ham license.
Most marine rigs -- in fact, all of them that I know about -- are capable of operating on the ham bands as well as the marine bands, though some may require special "programming".
The problem is, most marine SSBs although capable of operating on the ham bands are not very convenient. They don't have the frequency agility of ham rigs, with a few exceptions. The Icom 802 which is often advertised as being capable of both marine and ham operation indeed has a VFO which allows you to tune the bands, but it has detents and the architecture of the radio just isn't very intuitive to my mind. Many folks find it OK, though. It's probably what you're used to.
I routinely use an older marine SSB on the ham bands...a little-known Kenwood TKM-707. Great little rig. And, I choose to do so despite having at any time more than 20 other options: ham rigs, marine rigs, commercial rigs, and military rigs! I just love the 707.
On my boat, I have another little-know marine SSB: the Yaesu FT-600 alongside my Yaesu FT-900AT ham rig. It's also a fine little rig. See pic here: Gallery :: Miscellaneous 2007 :: NavStn_0140