If there is no driver handling the PCI card it would be possible to access it using ioperm (or iopl - depending on the address) if only port accesses are required.
Using DMA and interrupts is definitely impossible without a kernel-mode driver.
By googleing I found some text about something like a "generic kernel-mode driver" that allows writing user-mode drivers (including DMA and interrupts).
You should ask your customer which kind of kernel-mode drivers for accessing PCI cards is installed on the Linux board.