It's possible, but with all due respect, I do not believe this is likely. For example, when I have received the Precious Blood, I commonly have a bit left over on my bottom lip. I believe what happens is, due to the circular shape of chalices, and since it's difficult to completely wrap your lips around the arc due to its thin metallic surface, some of the Blood washes around the outside of your upper lip and onto your bottom lip as you are receiving.
This has been my experience when receiving the Blood (which is why I don't do it very often), but maybe others wrap their lips tightly enough around the rim that there is no spillover. I don't see how though, because every time I've tried to do so tightly enough, the rim of the metallic chalice almost cuts my lip open. And I've still failed every time.
So, since it was on my bottom lip after receiving, then it's likely some of it was left on the outside rim of the cup. Also, due to capillary action, as the chalice is wiped, some of the Blood will flow through the cloth and thus, eventually touch the outside rim as well.
These are my thoughts and why I don't feel squeamish receiving from a cup some stranger also touched with their mouth. However, as you said, Christ is complete in the Host so it's not a point to truly argue about. My thoughts immediately went to those with gluten allergies when the temporary prohibition was announced, and I do truly feel sorry for such people in this circumstance.
Let me explain.
First of all, I worked banquets and cleaning rooms in hotels in college. We washed glasses with industrial cleaner before machine washing. The reason being was lipstick. A syphilis virus can live through two machine washings living in lipstick. I’m sure the flu virus is no different.
Second, I wash altar linens. They must be pretreated because of the amount of lipstick on them. An EMCH wipes the rim of a cup with a dry cloth. This spreads any germs around that rim.
So lets look at this scenario. Congregant A drinks from a communial cup and puts her lipstick smear on the rim. EMHC wipes the rim, sending lipstick around it. Congregant B walks up with the flu. His lips touch and leave the virus. The EMHC then wipes again, spreading the virus around the cup and into the lipstick while turning the cup. The virus is now at the top. Congregant C sips and the cup is wiped and turned. Congregant D now sips. The lipstick holding the virus is now on his bottom lip, to be licked. The wine will not kill what is encased in lipstick because there is no degreasing agent.
Along with that, Altar Wine has a 10% alcohol content and is not pure at that. It’s water AND wine. It takes 40% ethanol alcohol to kill a virus according to the CDC.
http://www.cdc.gov/ncidod/EID/vol12no03/05-0955.htm
Avoid the cup.