Very likely. WWI was at the early stages of chemical warfare, so it wasn't as though things like nerve gas were heavily in use. Instead, the most common chemical weapons were generally asphyxiating agents (chlorine, phosgene), blister agents (mustard gas), and lachrymator agents (tear gas). All of these can cause damage to the lungs, the most heavily used (mustard gas, chlorine, and phosgene) were especially damaging to lung tissue. Inhaling chlorine gas produces hydrochloric acid, causing direct chemical burns on lung tissue. Mustard gas is a blister agent and causes blistering of skin and, if inhaled, the lungs: on lung tissue it also has a mutagenic effect, resulting in increased risk of cancer and life-long cellular damage. Phosgene chemically disrupts the functioning of alveoli in the lungs, which typically results in pulmonary edema, inflammation, and severe coughing which produce long lasting scar tissue and reduced lung function.

All of which would likely increase case fatality rates for a disease such as the 1918 H1N1 flu which often caused death through pulmonary edema. It's worth pointing out that for every person killed by chemical weapons in WWI many others would typically have been exposed and survived, because the nature of the chemical agents used were such that lethality was a matter of dose, and most battlefield conditions as well as most deployments were sub-optimal to maximize lethality.

However, there are many confounding factors. For one, transmission among soldiers was one of the ways the flu spread so rapidly initially. If more soldiers were infected, you'd expect them to be a larger proportion of the overall fatalities. Additionally, it seems that there was an increase in mortality for more youthful adults. Possibly this was due to the way the flu often killed by overcharging the host's immune system in a "cytokine storm", which would result in higher mortality rates in individuals with stronger immune systems. Since a good fraction of the under 30 population were enlisted in armed forces at the time due to widespread conscription, the mere age bias of the disease could have resulted in soldiers being over-represented as victims of the disease as well.

Additionally, food shortages were very common especially in Europe during and just after the war. Germany was subjected to a naval blockade by the British Royal Navy which cut off much of their food imports, reducing their overall food production. Additionally, along with the imposition of rationing in Germany the once ubiquitous potato was replaced with turnips (leading to a period of time called the Turnip Winter). Turnips are harder to digest and less nutritious than potatoes (they contain fewer vitamins, for example), which contributed to an even greater degree of malnutrition and vulnerability to disease. But food shortages and malnutrition were widespread near the end of the war, existing in Russia, Austria-Hungary, Belgium, The Ottoman Empire, Lebanon, Iran, and German East Africa. These more serious famines, which collectively caused millions of deaths, overshadowed the less severe but still concerning increases in food insecurity happening almost everywhere across Europe (partly due to disruptions by the war, partly due to interdiction of food at sea through unrestricted submarine warfare, partly due to taking large volumes of food explicitly for military use).

Malnutrition is far and away probably the most important comorbidity contributing to increased death rates for infectious diseases (of any sort), so, yes, those statements are accurate.

What we don't know and don't really have enough data to prove is how much of a factor either played. We can hand-wave and say both factors increased fatalities, but we don't really know if they increased fatalities by, say, an excess of 20% or by a factor of 2 to 3x. Either number is within the range of plausability.

One thing that is worth pointing out here, though, is that even without those contributing factors, the 1918 flu pandemic would still have killed an enormous number of people. It was highly transmissible and fairly infectious (about as infectious as a typical flu, which is enough to infect about 10-20% of the entire world population within about a year) and it had a high case fatality rate of at least single digit percentages even in healthy people.