You use the phrase, "system has motherboard hardware controller". Probably not exactly right. I presume you're talking about a very common current system which has "RAID built into the motherboard". In fact, the RAID system is software resident in the BIOS, rather than separate dedicated RAID controller hardware.
By the way, no, the disks and their data are NOT independent of the controller. Whether the control of the RAID array is by software or hardware, each RAID controller maker seems to have their own flavor and it is not common for a disk set made on one controller to be usable with another controller. In some cases, even different controller models from the same manufacturer are "incompatible". There are exceptions to this - see my next paragraph about nVidia as an example. But another way people address this is to insist on using an add-on hardware card, rather than the mobo's built-in system. The idea is that if the mobo craps out you simply get another and move the RAID controller card. And if the card fails, you buy another just like it, making sure the new one is "compatible" with the old one.
Anyway, you're talking about RAID1 in particular. I'm not positive about this, but I thought that some mobo's and HDD controllers cannot read one of the disks from a RAID1 array from another machine because they can't recognize some of the Partition Table data to understand the disk. However, some can do this, especially if machine #2 has the same mobo chipset as machine #1. In your case, check carefully into the details of what chipset your mobo has, and what the chipset manufacturer's website has to say about this question. I know that one of my machines has a nVidia chipset and their website claims that ALL of their recent RAID controller systems use exactly the same algorithms so that you can get away with moving a RAID array disk set from one machine to another (IF they both have nVidia chipsets) and it will be usable on Machine #2.
With RAID1 there is a clean way to do what you want. Read the RAID manual for your system fully. In mine there is a menu choice to break the RAID1 array. What this does is re-mark some info on the two drives so that they become independent "normal" (non-RAIDed) drives, and at least one of them (maybe both) has ALL the info on it so it can be moved and used in any other machine. Now, IF your system will do this and make BOTH drives useable independently with all their info, you could do this breakup, stash one in a safe place, and then use the second drive as a new master (along with a new third drive) to create a new RAID1 array based on the info on that master.
Even if breaking the array produces only one disk with all the info intact, you could do something similar. Break the array, then remove the disk with all info. Install a third disk and create a new array, empty. Re-install the disk with all data as a "normal" disk, then copy everything over to the new array. Un-install the original disk and stash it in a safe place.
However, if your original aim was to make a good backup, this seems a complicated way to proceed.