Yes, the unit doesn't really distinguish from what is the host and what is not.
The human body is full of other organisms, some are parasitic while others are symbiotic and others just bacteria like those that help us digest food. Each with their own DNA but in order for the host to function as normal and not be altered these organisms must remain in the host.
Remember, prior to bonding to a human host the Unit has no idea how a human is put together or how we work.
The Unit does prevent anything new though so from the point of bonding on the host has a super immune system thanks to the Unit but anything prior to bonding would not necessarily be removed.
For example we know for a fact the unit does not remove scars or even cloths from the host.
Not to mention the problem with diseases like HIV is because the body does not recognize it as foreign, in fact it infects the white blood cells to produce more of itself and that causes the immune system to attack itself which then renders the victim without an immune system and thus people die from all the diseases we are normally immune against.
HIV itself doesn't kill us, AIDS is just us being attacked by everything that we are normally immune against.
So there is no guaruntee that the Unit would remove such an infection, but the Unit will prevent it getting worse and allow the host to live with it.
Really, the idea that the Unit is a cure all is pure speculation.