Diet Pepsi is sweetened with sucralose (diet coke is sweetened with aspartame). Sucralose ha been found in studies to not affect blood sugar levels:
This study demonstrated that, similar to cellulose, sucralose consumption for 3 months at doses of 7.5 mg/kg/day, which is approximately three times the estimated maximum intake, had no effect on glucose homeostasis in individuals with type 2 diabetes. Additionally, this study showed that sucralose was as well-tolerated by the study subjects as was the placebo.
Lack of effect of sucralose on glucose homeostasis in subjects with type 2 diabetes
Diet Pepsi contains about 40 mg of sucralose per 8 ounces (about 250 milliliters). At 4 liters per day, that's about 640 mg of sucralose, and at a weight of 125 kilograms that's equivalent to about 5 mg/kg/day, less than the 7.5 mg/kg/day in this study.
Since that study might be called biased because of the funding, here's another one, where patients received a one time dose of 1 gram of sucralose that had no effect on blood sugar: Glycemic Effect of a Single High Oral Dose of the Novel Sweetener Sucralose in Patients With Diabetes
However, 4 liters of Diet Pepsi puts your relative at the upper limit of the Acceptable Daily Intake as defined by the FDA, which is 5 milligrams per day and kilogram. From the FDA:
Generally, an additive does not present safety concerns if the estimated daily intake is less than the ADI.
Your relative might want to reduce his intake. Reducing his intake to a maximum of two instead of four liters would put him firmly below the ADI. Four liters od a pretty high intake of fluids anyway. If this is because of thirst, that in itself is a sign of badly managed diabetes and requires medical attention.
In summary, no, noone can say that drinking diet drinks is completely safe. That's true of most substances, and so far sucralose has not shown to be unsafe. It is generally thought to be better for diabetes patients than drinking sugar-sweetened drinks which make blood sugar control harder. The American Diabetes Association lists diet drinks on their page on What to Drink?, alongside, of course, unsweetened beverages, which are preferable.
But I'd estimate that the smoking and weight puts him more at a health risk than the Diet Pepsi. Smoking and diabetes have been shown to be major health risk. Your relative hopefully has a doctor who knows how to treat diabetes, and needs to talk to them about how to control the diabetes.