No, you can't use Intel ICHR raid for vSphere/ESXi. The reason for this is because the raid doesn't exist as a volume to be exposed through a controller driver (the real explanation for what all the kids call "fakeraid").
All RAID solutions are software-based, but what most call "hardware RAID" are solutions where the RAID software runs on the controller ("firmware") and so when you use a driver to allow your O/S (ESXi in this case) to see the volumes (non-RAID such as SATA, IDE, or Host Bus Adapters aka HBAs expose drives instead of volumes), then the O/S has a lot less work to do that with a more typical software RAID solution. ICHR is an interesting hybrid solution where the SouthBridge chipset actually does provide firmware for the RAID and a BIOS where you can do some basic configuration. It does not provide a proper INT19 bootstrap loader and that means that the RAID volumes it presents can't be booted off of and in effect, don't really exist until the IAStor service starts, uses the ICHR driver to see the volumes, THEN presents them to the O/S.
Windows can deal with this through its bootloader process and I imagine VMWare could as well but they never will because as others have pointed out, ICHR RAID isn't "pro grade" due to its lack of a dedicated parity processor (ICHR uses your x86 CPU which actually does an outstanding job when setup right) and the inherent dangers in that such as the fact that your CPU is a general purpose processor doing many other things making it FAR more prone to crashing than a dedicated parity processor. The lack of certain cache/buffers and proper battery-backup for uncommitted transactions also make ICHR high-risk compared to "hardware RAID" solutions.
In the end ICHR is a value-added solution for people who don't need 6 9's (99.9999%) of uptime and can risk downtime and minor data loss. If you want to play with a really interesting solution, get a community license for NexentaStor 3.x, install vSphere on any drive/array you can get your hands on, create a VM for NexentaStor and install it, learn how to do RDM (Raw Device Mapping) and expose your drives to your NexentaStor VM through RDM, then expose NFS of iSCSI from THAT VM to the same host and use that SAN solution for your other VMs and other systems on your network. That way you can take advantage of raw disk performance, ZFS (RAIDz and the likes), and learn all kinds of cool things about enterprise SAN use with vSphere and virtualization. It's a project but done right (throw a couple 60GB SSDs in strategically for cache/ZIL) you will learn a lot, and have extremely flexible, portable, and expandable storage thats hardware agnostic.