Yes, this is completely possible and also reasonably common.
IP over IB (IPoIB) is well supported in several OS's, including Windows, Linux (Red Hat/CentOS/SL/Debian/etc). Communication between OS's using IPoIB works very well, since (after the Infiniband drivers are installed) the OS's just see the traffic like normal ethernet.
(actually, that's a bit of a simplification, as you can go into the Infiniband settings on your OS's to tweak things for extra efficiency if you want, but the concept of "it's just like normal ethernet" is correct)
There are also other Infiniband protocols (not just IPoIB) which take advantage of Infiniband's special properties more (mostly RDMA). Things like SRP (a block storage protocol), iSER (iSCSI protocol enhanced for RDMA), and so on. These other protocols aren't as widely spread across all versions of all OS's as IPoIB, so some combinations works well, others not so much. But they're worth knowing about and looking into, depending on what you're thinking of using Infiniband for.
Does that helps?