Yeah, but, like i said, that works even without that being a power of the "parasite"...Well be aware my assumption was assuming this character is truly HIVE from the comics. The villain Viper at one point is killed by Leviathan and the leaders of Hydra come across her bullet ridden corpse. Hive quickly reanimated her with his parasites, which latched to her brain. Later on, she was able to remove the parasites with the help of HAMMER but remained alive.
Think of it this way, in the body of Will the parasite was not exactly a powerful fighter. His fight with Fitz was mostly bumbling around because of the leg wound and the fact Will was not much of a combat expert. This means the parasite may rely on the abilities of it's host, rather then adding anything of it's own.
Now he has the body, and likely memories, of Grant Ward, a deadly assassin who was said to be on the same level as Black Widow. This is likely why Malick sent Grant Ward in the first place, knowing he was the only one "worthy" to become the parasites next host. HYDRA will likely do everything in their power to heal up Wards body so that the parasite can have his strength secured.
While the thing itself showed no signs of healing the vessel.