sd, it's an old thread but the question is still relevant.
I know folks who are on coumadin aka warfarin and other "blood thinners". Yo need to treat them the same way that you would treat any other natural "bleeders" (hemophiliacs) on the boat. An injury or bruise needs to be treated promptly and properly.
For cuts and gashes, there are some marvelous new products (refined from battlefiled medicine) like names like "Quik Clot" that can be poured on a wound to clot it almost normally and immediately. A good thing to have in any boating first aid kit anyway.
For bruises, you need to have ice packs available (chemical "slap" packs will do) and apply them immediately, and elevate the area.
There are also injections that can be given (something like Vitamin K) that rapidly increase clotting ability but that of course will need an RX to be added to the med kit, and some training.
All in all...if you are prepared for trauma (as opposed to simple bandaiding) you can deal with bleeders, but the decision about what kind of crew med risks you are willing to take is something else again, i.e. can you afford to have one crew out of action for 48+ hours at all?