I know raw eggs should be avoided, especially by sensitive people (children, pregnant women), as they may contain salmonella. Let's say I make a big tub of ice cream, with raw eggs, and several people have some with no ill effects - can I assume that this particular tub of ice cream is salmonella-free?
There is probably still some risk, so I wouldn't assume it was safe; however, ice-cream is frozen, so I wouldn't worry about ice-cream at all, unless the egg-mixture was left at room temperature for a significant time before freezing.
As far as I know, salmonella is in the faeces of the chicken, if present. Some faeces will often stick to the shell. In very rare circumstances, which I believe are negligible, the salmonella penetrates the shell and infects not only the white (less of a problem) but also the nutritious yolk, and then the whole egg is contaminated. But this chance is probably too small to encounter in one's average life time.
What has normally happened if the faeces are contaminated and people get sick, is that some of the salmonella present on the outside of the shell contaminates the egg when the shell is broken, or the extremely small number of bacteria present in the white get a chance to infect the whole egg (chance ca. 0.005 %, see below). (Note that in many countries the outside of the shell of supermarket eggs is supposedly sterilized.) At that very moment, however, the number of bacteria present in the egg white should still not be enough to make people sick. But if the egg is then left to sit outside the refrigerator for several hours, and enough faeces touched the egg white, the bacteria may have enough time to multiply and make you sick. If the egg is properly refrigerated, chances are much lower, but I do not know the exact numbers.
One often sees grey spots and smears on the outside of eggs; I believe this is normally chicken faeces. Even so, salmonella is quite rare, such that the healthy shouldn't be worried about making ice cream, mousse au chocolat, and such from unpasteurized eggs. But if a young child, an old person, a pregnant woman, or someone with health problems were to eat the ice cream, I would not take the chance and use pasteurized eggs. If the food is contaminated, the fact that people do not get sick who have eaten it immediately upon making it offers little evidence, because the bacteria haven't had the time to multiply yet. I believe you will normally not get sick from eating contaminated steak tartare, for example, because it is eaten immediately.
However that may be, ice-cream is frozen: as Derobert said below, salmonella probably cannot multiply below 5 °C, and certainly not below 0 °C, so ice-cream should be safe under all normal circumstances, that is, if it was frozen shortly after breaking the eggs. Normal temperatures in refrigerators slow down the growth of the bacteria as well: perhaps you shouldn't worry too much about anything that is kept at 7 °C anyway for a few days.
Short answer:no, has to do with exponential growth and also individual sensitivities.
Long answer: You only need a few bacteria to make you sick. And bacteria grow exponentially.
Let's assume that eating up to N1 bacteria won't do anything, N2 bacteria will give you a light fever, and N3 bacteria will send you to hospital. And N3 is a very low number. This source claims that 6 bacteria per serving are enough, and while we don't know how many servings each sick person ate, we can conclude that 100 bacteria is probably more than enough (15 servings at once!). Also, the difference between N1, N2 and N3 must be tiny: under perfect conditions (= in your intestines, at 37°C and surrounded by food), Salmonella numbers double every 20 minutes, which means that very small differences in the starting numbers will make the difference between one million or one billion bacteria a few hours later. And salmonella has an incubation period of up to 72 hours.
Imagine that person A eats a dish containing raw eggs, waits 72 hours (no symptoms in that time), and then person B eats the same dish. There are several scenarios in which person B might get sick.
Even if you have several people tasting first, their showing no symptoms can not be taken as a guarantee, especially if you know that person B is at higher risk (e.g. a small child). Also, I am sure that there must be more possible scenarios in which B gets sick, I just listed a few I could think of.
Instead of taking risks, I would advise that you prevent salmonella contamination and growth in the first place. You can kill salmonella with acid and heat, or you can make food without the eggs.