Does it matter if I sauté onions for high liquid foods?

It makes a big difference. The heat you can impart to anything by boiling is limited to 100°C (212°F). This is too low for some of the flavor magic to happen, like maillard reactions, which start about 140°C. A pan's temperature can get much higher than boiling water, which is why you saute them first. If you try to make onion soup without sauteing them first they'll soften, but they'll never lose that raw onion flavor, and you won't get the sweetness or depth of flavor from the maillard reactions.

It flavors your oil. Notice how in many soups there's glistening oil floating on the surface? It makes the soup taste better, but simply drizzling in the (neutral, in this case) oil at the end of cooking won't provide the same delicious results.

At my household we often make tomato egg-flower soup (or as other people will put it, tomato egg-drop soup), and it involves frying up diced tomatoes in some oil, before filling up the post with faucet water and letting it bring to a boil.

Like what you addressed in your post, no caramelization happened on the tomatoes (and predictably so, as they are really watery), but you can clearly see the orange-color (and flavored) oil that floats to the top when adding in the water.

I make soups both ways and there is a clearly different end result. I'm not sure the exact mechanisms going on but I'll list some hypotheses/thoughts:

• I'm sure if you boil the soup for a very long time any differences will approach imperceptibility, but many soups aren't cooked for a super long time.
• Anyone who has experimented with this knows that the texture of onions changes much faster when you are sautéing or sweating compared to boiling. Thinly sliced onions will still have some of their firmness even after an hour of a slow simmer.
• Even on low heat the cooking temperature will be much hotter than simmering water. Although you aren't cooking them long enough for caramelization / obvious Maillard reactions, you will still be introducing some of those flavor compounds into the mix.
• On the flipside, the heat of the initial sweat will also destroy some compounds present in raw onion, much like how raw garlic is different than sautéed garlic which is different from roasted garlic. Many recipes probably include a sweat purposefully to remove the "bight" you get from raw onion. Of course those flavor compounds may also be desirable for some dishes.
• Sweating also introduces evaporation, but this probably isn't one of the bigger factors.
• Finally, a lot of the above arguments also pertains to the oil as well. Olive oil that's been sautéed with something is going to taste differently in the end compared to just throwing it in while the soup is boiling. (As Anastasia Zendaya points out, the flavors of the thing you are sautéing will be added to the oil, but I'm focusing more on how the heat itself is changing the fat you are using).

I agree with the answers noting temperature and flavor. Fat carries flavor better than water.

To add another perspective, Salt Fat Acid Heat notes why not to cook onions in acidic liquids. (That may be the case if you are making, say, a tomato heavy stew):

Anything containing cellulose or pectin, including legumes, fruits, and vegetables, will cook much more slowly in the presence of acid. [...] The acid in tomatoes explains why those pesky onions float to the top of a pot of sauce or soup and stay there, never getting soft, even after hours of cooking.

Funny enough, I had just read this section and ran a small experiment to see if I could confirm it.

I boiled two sets of 70g of diced Spanish onion for three minutes. In the picture below, the onions on the left were cooked in 2 cups water, and the onions on the right in 1.75 cups water + .25 cups white vinegar.

Onions cooked in the presence of vinegar had more of a bite.