Yes, Boot Camp works with the Accelsior and a Radeon HD 5870 on a MacPro3,1 when you put the Accelsior in any other slot (4,3,1) than the one you would really want to use it in (slot 2). Go figure...
Booting OS X from the Accelsior is easy. Boot Camp does not affect being able to boot OS X. You just have to set the Startup Disk preference to the OS X partition on the Accelsior. However if the setting gets changed to something else, then you need to go through an extra step to get back to booting the OS X partition on the Accelsior.
Since the MacPro3,1's built in Startup Manager (hold option at startup) does not show the Accelsior partitions, you need another method to boot OS X from the Accelsior.
One alternative is to use rEFInd. But I think that will only show partitions on the Accelsior if rEFInd is installed on a partition on the Accelsior (I have to double check that) which means it could encounter the same problem as above.
So to solve this problem, you need to boot another installation of OS X or the OS X installer from one of the 4 internal drive bays, USB, FireWire, or DVD, and use the Startup Disk preferences panel to select the OS X partition on the Accelsior. I have another OS X partition for this purpose (and also to allow repartitioning of the disk containing my normal OS X boot). I think the Boot Camp control panel in Windows might be unable to see the OS X partition on the Accelsior (have to double check that too).
Note that the Startup Manager does not affect the startup disk preference. So you should use that to boot your Boot Camp partition. Then don't use the Startup Manager when you restart if you want to go back to OS X.
rEFInd is needed only if you have more than one Boot Camp partition on the same disk and want to use the boot loader on each partition. Otherwise, you would have one partition (the active partition) with a boot loader menu that lets you select from the other Boot Camp partitions. I use rEFInd to select between multiple OS X and Windows partitions on different disks (one disk has three versions of Windows and a couple versions of OS X).