You would very likely NOT be able to swap cards without reformatting your drives. It's technically possible, but the time spent doing it will quickly outweigh the time it would take for you to restore your data from backup. That is, unless you're moving to a similar controller, such as one of the same product family.
This controller, as many other do, stores its RAID abstraction information as metadata on all participating drives (plus a copy of it in the card firmware itself). This way, your array members may be moved to another controller and imported as a "foreign array" (copying their RAID metadata to the new card's firmware).
An 2TB disk limit is typically enforced by the use of an MBR as a disk label / partition table. The vast majority of RAID cards of the time (including this one) actually put a hidden partition table on these drives before making an arbirarily sized partition on that table to use as your RAID member, rather then the whole raw disk. This gave controllers new options for flexibility that previously weren't possible, such as multiple different kinds of arrays on the same sets of disks. The actual method for accomplishing this varies from vendor to vendor and card to card.
So moving your card to a new system may not enable you to use all 3TB of your disks, even if the firmware purports to support it. In that case, a complete metadata wipe (which can be done from the controller) of your RAID volume will have to come before making a new array and restoring from backup. Hopefully, your array uses a more advanced metadata structure and is only limited at the controller for 2TB size.
This firmware is proprietary, so I can't give you a definitive answer as to whether this will work. TL;DR: your mileage may vary. There's no sense in not trying ti if you can keep your service up and have current backups.
