Including initial I am saying that makes absolutely no difference to the syntax of the statement that follows. And made you more susceptible to infection is a pretty long verb phrase, so let's consider a simple one-word Present Tense verb (which again makes no difference to the syntax)...
1: Alcohol evaporates, as does water
2: Alcohol evaporates, as water does
In principle both the above are syntactically valid and mean the same - but version #1 is "marked" (it's an "unusual" form today, because in modern English the subject noun usually comes before the verb).
But in practice, this particularly subject/verb reversal has been retained as something of a "frozen form", so my example #1 is actually more common than #2. Note that this usage only applies after as - NOT after the near-equivalent like...
3: Alcohol evaporates, like does water <~~~ IDIOMATICALLY UNACCEPTABLE!
4: Alcohol evaporates, like water does
5: Alcohol evaporates, like water
Note example #5, showing that we can discard the auxiliary / helper verb does. Also note these two slightly different interpretations that could apply to all my examples (except #3, which is simply invalid)...
a:) Alcohol evaporates. Water also evaporates
b:) Alcohol evaporates. Water evaporates in the same way that alcohol evaporates
Since there's only really one way that liquids can evaporate, that's not a very meaningful distinction. But consider a slightly different context...
6: I eat fish, as do the Japanese
7: I eat fish, as the Japanese do
8: I eat fish, like the Japanese do
9: I eat fish, like the Japanese
Some native speakers would say that #6 is more likely to simply mean I eat fish. The Japanese also eat fish, whereas the others carry stronger implications that the way I eat fish (raw, using chopsticks) is similar to the way (stereotypical) Japanese do.
Some native speakers will also say it makes a difference whether I include a comma (pause, in speech) before as. But even if that's true, it doesn't invalidate the points I'm making here.
TL;DR: The construction [Subject1] [Verb] as does [Subject2] inverts the normal subject+_verb sequence for Subject2 and does. This was common in English back in Shakespeare's time, but it only survives today in certain specific contexts. Using it today is thus slightly "formal, literary". Consider...
10: I watch TV, as do you
11: I watch TV, as you do
12: I watch TV, like you [do]
All these examples mean (approximately) the same thing. But they're in decreasing order of formality.
