Sick meaning: the flu, viruses (like HIV), and cancer? From my understanding, no, Ricean vampires are not susceptible to these kinds of diseases. In Only Lovers Left Alive, those vampires have arrangements w/ mortal agents to get clean blood rather than risk taking victims, whose blood could be tainted w/ modern disease or drugs, which OLLA vampires are vulnerable to (but they don’t go into much detail about it). I can’t think of any other vampire media that even touches on the issue of blood diseases and/or other physical illnesses. 

@anton-mordrid makes an excellent point here [X]: #1 how the fuck can you not associate HIV/AIDS with vampires, you personally literally made it a blood disease transmitted by explicitly sexual acts between your gay male protagonists.

I’m not educated enough to go any further on this issue, but if you want more on this, go to @vraik and @anton-mordrid. 

Sick meaning: physically repulsed to the point of having a visceral reaction? Yes.

[^Horror Vacui, Exploring the darkness (2/?) by @sheepskeleton]

In TVL, Lestat tosses his cookies (ok he vomits some blood, no cookies tossed) at the sight of a pile of dead bodies the night he’s turned. (He also hurls as he’s escorted down to the Children of Darkness meeting).

“In a deep prison cell lay a heap of corpses in all states of decay, the bones and rotted flesh crawling with worms and insects. Rats ran from the light of the torch, brushing past my legs as they made for the stairs. And my nausea became a knot in my throat. The stench suffocated me.

He also says that vampires can’t stand to be around the dead bodies of their kills, either:

Revulsion at the sight or smell of death seemed part of my nature. I couldn’t watch executions any more than when I was that trembling boy from the Auvergne, and corpses made me cover my face. I think I was offended by death unless I was the cause of it! And I had to get clean away from my dead victims almost immediately.

Dead blood is not poisonous to them, just distasteful. In TVL, Lestat goes to Armand in Paris for help after Claudia and Louis try to assassinate him a second time, and Armand throws him in a locked cell with a dead mortal for dinner: “Sometime in the dark, I discovered a mortal victim there. But the victim was dead. Cold blood, nauseating blood. The worst kind of feeding, lying on that clammy corpse, sucking up what was left.”

^So clearly dead blood is not bad in the sense of being poisonous, just icky 😛