Yes, the Claw gives you a 35% chance to cause a bleeding wound on hit so it will work for the purpose of Taste for Blood and will stack with any other melee related bleeding source. The second on hit effect is 35% to cause a contamination debuff (10% extra damage - stacks up to 20 (!)times) which is not the same as bleeding and is also not to be confused with infected wound that is related to bleeding caused by the Vile Weaponry feat.
As a good alternative there is the Ripper's glove. It has a 3 times 25% chance to cause a bleeding wound. How much is that? You can calculate like this: there is a 75% chance NOT to cause bleeding and you multiply it by 3:
0.75 x 0.75 x 0.75 = 0.42 chance NOT to cause bleeding, or in other way, it's a 58% chance to make a bleeding wound on every hit. That's much better than 35% of the Claw but it doesn't have the contatination chance.
So which one is better depends mostly on how many enemies you're battling and the rest of your gear. If you don't use metal armor with serrated blades or bladed boots for additional chance to cause bleeding and are against thrash mobs that won't last long anyway, than the Ripper's glove is probably better as it will allow you to stack Taste for Blood much faster. In all other cases and against really tough opponents the Claw wins when it comes to total debuffs.
I wouldn't put them in both weapon slots at the same time though. You need one weapon for the debufs, and the other for damage. Works extermly well for hybrids like strength based sledgehammer builds who also have 8-10 dexterity and important unarmed feats like Lightning Punches, Wrestling and Combo. Soften em up with the ripper's glove, possibly stun and cause mayhem with the sledgehammer. I play one right now and it's one of my strongest playthroughs.