Maybe. According to this paper (pdf) by Jonathan Klick and Joshua Wright, San Francisco experienced a spike in ER visits from food-borne illness when it adopted its ban in 2007. From the paper's introduction:
In an effort to reduce litter and protect marine animals, jurisdictions across the globe are considering banning plastic grocery bags. In the US, California leads the way. San Francisco enacted a county-wide ban covering large grocery stores and drug stores in 2007. It extended this ban to all retail establishments in early 2012. Los Angeles followed suit in 2012, as did a number of smaller cities throughout the state. Some municipalities have imposed taxes on the bags rather than implement direct bans.
These bans are designed to induce individuals to use reusable grocery bags, in the hope that a reduction in the use of plastic bags will lead to less litter. Recent studies, however, suggest that reusable grocery bags harbor harmful bacteria, the most important of which is E. coli. If individuals fail to clean their reusable bags, these bacteria may lead to contamination of the food transported in the bags. Such contamination has the potential to lead to health problems and even death.
We examine the pattern of emergency room admissions related to bacterial intestinal infections, especially those related to E. coli around the implementation of the San Francisco County ban in October 2007. We find that ER admissions increase by at least one fourth relative to other California counties. Subsequent bans in other California municipalities resulted in similar increases. An examination of deaths related to intestinal infections shows a comparable increase.
Using standard estimates of the statistical value of life, we show that the health costs associated with the San Francisco ban swamp any budgetary savings from reduced litter. This assessment is unlikely to be reversed even if fairly liberal estimates of the other environmental benefits are included.
This is a small sample, obviously, so I take it as only weak evidence for a causal effect. But one reason the result is at least plausible is that reusable grocery bags can be nasty things:
Williams et al (2011) randomly selected reusable grocery bags from consumers in grocery stores in Arizona and California. They examined the bags, finding coliform bacteria in 51 percent of the bags tested. Coliform bacteria were more prevalent in the California bags, especially those collected in the Los Angeles area. E. coli was found in 8 percent of the bags examined. The study also found that most people did not use separate bags for meats and vegetables. Further, 97 percent of individuals indicated they never washed their reusable grocery bags. Bacteria appeared to grow at a faster rate if the bags were stored in car trunks. This study suggests there may be large risks associated with using reusable grocery bags, though it does imply that fastidiously washing bags can virtually eliminate the risks. However, the survey results suggest that virtually no one washes these bags.
Again, this may be a mere coincidence rather than a real phenomenon. It will be interesting to see whether Brackenridge and Dell see a spike in food-poisoning cases after our bag ban goes into effect in March. If a real phenomenon, will Austin see more or less illness than San Francisco? On one hand, Austin's ordinance is actually a good bit more stringent than San Francisco's 2007 ordinance, which permitted the distribution of recyclable paper bags and compostable plastic bans, and which did not even apply to all grocery stores in the city. Our Council really, really wants Austinites to use reusable bags. On the other hand, a lot of Austinites shop at suburban grocery stores that aren't subject to the ban.
Frequently discarding used bags and buying "fresh" reusable bags may be a wise precaution, regardless. It's true that will wipe out the alleged environmental benefit of using reusable bags, but that benefit is minimal anyway if you're not a litterer.