Weeds - Spoilers Inside

[Securb]

Would it be possible to harvest the yeast from such an infection and use it for making beer?

Yes you could -from Wiki:

Sugars assist the overgrowth of yeast, possibly explaining the increased prevalence of yeast infections in patients with diabetes mellitus, as noted above. As many Candida spp. reside in the digestive tract, dietary changes may be effective for preventing or during a Candida infection. Due to its requirement for readily-fermentable carbon sources, such as mono- or dimeric sugars (e.g., sucrose, glucose, lactose) and starch,